Project Euclid Problem is SOLVED!!!

https://projecteuler.net/problem=26

Using the fantastically potent FOSS CAS Maxima/wxMaxima the solution
is a fucking snap:

max:1$
maxd:3$
for num:3 thru 1000 step 1 do (
d:1,
fact_list:ifactors(num),
for i:1 thru length(fact_list) do (
if not(fact_list[i][1] = 2 or fact_list[i][1] = 5) then d:d*fact_list[i][1]^fact_list[i][2]
),
if not(d = 1) then (
rep:zn_order(10,d), print("denom = ", num, "repeats = ", rep),
if (rep > max) then (max:rep, maxd:num)
)
else (print("denom = ", num, "terminating"))
);
print("Max rep =", max, "at denom =", maxd);

The output is not ideal, but hey, I am a fucking messy eater.
I spill my coffee. I slobber all over my shirt. But I ALWAYS
get the correct answer in the most efficient way and that's
ALL that matters.

Hail Linux!

Hail GNU, FOSS, and the FSF!

Hail Stallman!

On Sat, 09 Mar 2024 13:28:40 +0000, Farley Flud wrote:

> Project Euclid Problem is SOLVED!!!
>

I got that wrong. It's "Project Euler Problem 26."

>
> Hail Linux!
>
> Hail GNU, FOSS, and the FSF!
>
> Hail Stallman!
>

But I got this right.

Ha, ha, ha, ha, ha, ha, ha, ha, ha!

On Sat, 09 Mar 2024 13:28:40 +0000, Farley Flud wrote:

> Project Euclid Problem is SOLVED!!!
>
> https://projecteuler.net/problem=26
>

1000? Why stop at a measly-peasly 1000? Let's do 100,000.

Just paste the following maxima code into a "file.mac"
and then copy the file into the maxima search path.

Then, from maxima (not wxMaxima) do:

load("file.mac");

Wanna go for 1 million? 10 million? A billion?

It's no problem. Just change the "for" loop maximum,
but you'd better also compile the code for faster
execution.

==============================================================
file_output_append:true;
f:"/some/path/prob26.txt";
max:1$
maxd:3$
for num:3 thru 100000 step 1 do (
d:1,
fact_list:ifactors(num),
for i:1 thru length(fact_list) do (
if not(fact_list[i][1] = 2 or fact_list[i][1] = 5) then d:d*fact_list[i][1]^fact_list[i][2]
),
if not(d = 1) then (
rep:zn_order(10,d), with_stdout(f,print("denom = ", num, "repeats = ", rep)),
if (rep > max) then (max:rep, maxd:num)
)
else with_stdout(f,(print("denom = ", num, "terminating")))
);
with_stdout(f, print("Max rep =", max, "at denom =", maxd));
================================================================================

>
> Hail Linux!
>
> Hail GNU, FOSS, and the FSF!
>
> Hail Stallman!
>

On 3/9/2024 7:28 AM, Farley Flud wrote:
> Project Euclid Problem is SOLVED!!!
>
> https://projecteuler.net/problem=26
>
> Using the fantastically potent FOSS CAS Maxima/wxMaxima the solution
> is a fucking snap:
>
> max:1$
> maxd:3$
> for num:3 thru 1000 step 1 do (
> d:1,
> fact_list:ifactors(num),
> for i:1 thru length(fact_list) do (
> if not(fact_list[i][1] = 2 or fact_list[i][1] = 5) then d:d*fact_list[i][1]^fact_list[i][2]
> ),
> if not(d = 1) then (
> rep:zn_order(10,d), print("denom = ", num, "repeats = ", rep),
> if (rep > max) then (max:rep, maxd:num)
> )
> else (print("denom = ", num, "terminating"))
> );
> print("Max rep =", max, "at denom =", maxd);
>
>
> The output is not ideal, but hey, I am a fucking messy eater.
> I spill my coffee. I slobber all over my shirt. But I ALWAYS
> get the correct answer in the most efficient way and that's
> ALL that matters.
>
> Hail Linux!
>
> Hail GNU, FOSS, and the FSF!
>
> Hail Stallman!
>

I don't understand. You say it's solved. So what did your code find?
Which denominator under 1000 gives the longest repeating decimals if
numerator is 1?

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On Sat, 9 Mar 2024 13:37:52 -0600, Physfitfreak wrote:

>
> I don't understand. You say it's solved. So what did your code find?
> Which denominator under 1000 gives the longest repeating decimals if
> numerator is 1?
>

You have to enter this code into Maxima/wxMaxima and then you'll
see the complete answer.

But, for those that, for whatever reason, can't do it, the answer is this:

Max rep = 982 at denom = 983

Thus, the fraction 1/983 has a repeating decimal of length 982.

For proof, here is the decimal expansion (to 2048 places):

0.001017293997965412004069175991861648016276703967446592065106815869786368260427263479145473041709053916581892166836215666327568667344862665310274669379450661241098677517802644964394710071210579857578840284842319430315361139369277721261444557477110885045778229908443540183112919633774160732451678535096642929806714140386571719226856561546286876907426246185147507629704984740590030518819938962360122075279755849440488301119023397761953204476093591047812817904374364191251271617497456765005086469989827060020345879959308240081383519837232960325534079348931841302136317395727365208545269582909460834181078331637843336724313326551373346897253306205493387589013224821973550356052899287894201424211597151576805696846388606307222787385554425228891149542217700915564598168870803662258392675483214649033570701932858596134282807731434384537131230925737538148524923702950152594099694811800610376398779247202441505595116988809766022380467955239064089521871820956256358087487283825025432349949135300101729399796541200406917599186164801627670396744659206510681586978636826042726347914547304170905391658189216683621566632756866734486266531027466937945066124109867751780264496439471007121057985757884028484231943031
5361139369277721261444557477110885045778229908443540183112919633774160732451678535096642929806714140386571719226856561546286876907426246185147507629704984740590030518819938962360122075279755849440488301119023397761953204476093591047812817904374364191251271617497456765005086469989827060020345879959308240081383519837232960325534079348931841302136317395727365208545269582909460834181078331637843336724313326551373346897253306205493387589013224821973550356052899287894201424211597151576805696846388606307222787385554425228891149542217700915564598168870803662258392675483214649033570701932858596134282807731434384537131230925737538148524923702950152594099694811800610376398779247202441505595116988809766022380467955239064089521871820956256358087487283825025432349949135300101729399796541200406917599186164801627670396744659206510681586978636826042726347915

On 3/9/2024 2:37 PM, Physfitfreak wrote:
> On 3/9/2024 7:28 AM, Farley Flud wrote:
>> Project Euclid Problem is SOLVED!!!
>>
>> https://projecteuler.net/problem=26
>>
>> Using the fantastically potent FOSS CAS Maxima/wxMaxima the solution
>> is a fucking snap:
>>
>> max:1$
>> maxd:3$
>> for num:3 thru 1000 step 1 do (
>>      d:1,
>>      fact_list:ifactors(num),
>>      for i:1 thru length(fact_list) do (
>>      if not(fact_list[i][1] = 2 or fact_list[i][1] = 5) then
>> d:d*fact_list[i][1]^fact_list[i][2]
>>        ),
>>      if not(d = 1) then (
>>          rep:zn_order(10,d), print("denom = ", num, "repeats = ", rep),
>>          if (rep > max) then (max:rep, maxd:num)
>>      )
>>      else (print("denom = ", num, "terminating"))
>> );
>> print("Max rep =", max, "at denom =", maxd);
>>
>>
>> The output is not ideal, but hey, I am a fucking messy eater.
>> I spill my coffee.  I slobber all over my shirt.  But I ALWAYS
>> get the correct answer in the most efficient way and that's
>> ALL that matters.
>>
>> Hail Linux!
>>
>> Hail GNU, FOSS, and the FSF!
>>
>> Hail Stallman!
>>
>
> I don't understand. You say it's solved. So what did your code find?
> Which denominator under 1000 gives the longest repeating decimals if
> numerator is 1?

So as not to ruin it for those trying it in the future, you don't
publish the solutions to ProjectEuler problems. You submit your
solution to the website and it says if you're right or not.

Feeb's a prick, though, and published the code.

On Sat, 9 Mar 2024 15:03:27 -0500, DFS wrote:

>
> So as not to ruin it for those trying it in the future, you don't
> publish the solutions to ProjectEuler problems. You submit your
> solution to the website and it says if you're right or not.
>

Ha, ha, ha, ha, ha, ha, ha, ha, ha!

Ain't no fucking picayune bullshit website gonna tell *ME* if I am right.

I am *ALWAYS* right. ALWAYS.

Fuck that "Project Euler." It's only for asshole string manipulators using
bullshit Python.

Le 09-03-2024, DFS <nospam@dfs.com> a écrit :
>
> Feeb's a prick, though,

Yes.

> and published the code.

He was probably unable to code it himself. So it means the code is
already available somewhere. And as he was able to found it, it means
it's not too difficult to find. So it didn't spoil as much as he wanted
to.

--
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On 3/9/2024 2:01 PM, Diego Garcia wrote:
> You have to enter this code into Maxima/wxMaxima and then you'll
> see the complete answer.

Sadism :)

That Coke contest, which turned out requiring ordering from Walmart
before it happens.

But thanks for the answer.

It's not clear what algorithm you used that was better than brute force,
but brute force also is not that bad in this case. There aren't that
many denominators under 1000 that have primes other than 2 or 5 as
factors. That reduces the loop count dramatically. And among what
remains, one can eliminate, very fast, cases of low number of repeating
decimals unless a very large number is stumbled upon early in the loop.

Then the brute force on the remainder of the cases will advance pretty
well to find the longest repeating decimals.

I was expecting that some cases would have repetitions much larger than
982 decimals, so I'm kind of suspicious of the answer you got. But I
can't think of a way to test its accuracy in being the maximum.

I wish there was a chart I could look up, giving denominator integers
(with prime factors other than 2 and 5) as its x axis and max number of
repeating decimals as the y axis. With x interval going to about a
million or even a billion. It probably would need to be a logarithmic
chart to contain the results in a page. But one could get a nice idea
how this thing goes by taking a look at that. Are there surprises early
on for smaller integers, or big numbers begin to show only later on in
the chart for larger integers. If such plot doesn't show surprises, then
I'd take your result as accurate. Otherwise, it remains suspect to me.

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On 3/9/2024 2:42 PM, Physfitfreak wrote:
> And among what
> remains, one can eliminate, very fast, cases of low number of repeating
> decimals unless a very large number is stumbled upon early in the loop.

No, I meant to say the opposite. Replace the "unless" with "if". But
even then, I don't think it matters much where the highest number is, as
far as amount of computation is concerned.

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Le 09-03-2024, Diego Garcia <dg@chaos.rocks> a écrit :
> On Sat, 9 Mar 2024 15:03:27 -0500, DFS wrote:
>
>>
>> So as not to ruin it for those trying it in the future, you don't
>> publish the solutions to ProjectEuler problems. You submit your
>> solution to the website and it says if you're right or not.
>>
>
> Ha, ha, ha, ha, ha, ha, ha, ha, ha!
>
> Ain't no fucking picayune bullshit website gonna tell *ME* if I am
> right.

I'm not that surprised by your reaction. As you already said you shit in
your basement, it's not surprising you shit in others' places.

> I am *ALWAYS* right. ALWAYS.

You are wrong, but you are too retard to be able to understand why.

> Fuck that "Project Euler." It's only for asshole string manipulators
> using

You believe you are strong, but you show only how an asshole you are.

> bullshit Python.

Don't be too harsh on python. Last time you checked, you had 5, five,
yes FIVE, versions of python on your own computer. For someone who pretend to
master his computer and to hate python, it tells a lot.

I have nothing against python, my computer runs fine and I have only one
version of python.

--
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On 3/9/2024 2:42 PM, Physfitfreak wrote:
> I wish there was a chart I could look up, giving denominator integers
> (with prime factors other than 2 and 5) as its x axis and max number of
> repeating decimals as the y axis.

Another fucking mistake. Delete the word "max" from it. I type too fast
before process of thinking is over.

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Le 09-03-2024, Physfitfreak <Physfitfreak@gmail.com> a écrit :
> On 3/9/2024 2:01 PM, Diego Garcia wrote:
>> You have to enter this code into Maxima/wxMaxima and then you'll
>> see the complete answer.
>
> Sadism :)

No. It's another way to say he's too stupid to explain something he
can't understand. It's just a proof he was lucky to find the answer
somewhere on Internet.

--
Si vous avez du temps à perdre :
https://scarpet42.gitlab.io

On Sat, 9 Mar 2024 14:42:56 -0600, Physfitfreak wrote:

>
> I wish there was a chart I could look up, giving denominator integers
> (with prime factors other than 2 and 5) as its x axis and max number of
> repeating decimals as the y axis. With x interval going to about a
> million or even a billion.
>

There's no need to wish. Use my code. It's FOSS and free for all.

You can print any number of denominators and then make your own chart.

On 09 Mar 2024 20:55:19 GMT, Stéphane CARPENTIER wrote:

>
> Don't be too harsh on python. Last time you checked, you had 5, five,
> yes FIVE, versions of python on your own computer. For someone who pretend to
> master his computer and to hate python, it tells a lot.
>

That's Gentoo, honey.

I got 3 but I could have 10, 20, or a billion.

I can select:

[~]# eselect python list
Available Python interpreters, in order of preference:
[1] python3.11
[2] python3.12
[3] python2.7

Python 3.11 is first because that is the current Gentoo
default. But I can switch between all versions at will
via:

eselect python [1 | 2 | 3]

Can you do that with your crippled distro?

Ha, ha, ha, ha, ha, ha, ha, ha, ha, ha, ha!

On 3/9/2024 3:14 PM, Larry "The Prick" Piet wrote:

> On Sat, 9 Mar 2024 15:03:27 -0500, DFS wrote:
>
>>
>> So as not to ruin it for those trying it in the future, you don't
>> publish the solutions to ProjectEuler problems. You submit your
>> solution to the website and it says if you're right or not.
>>
>
> Ha, ha, ha, ha, ha, ha, ha, ha, ha!
>
> Ain't no fucking picayune bullshit website gonna tell *ME* if I am right.

> I am *ALWAYS* right. ALWAYS.

You're a lying joke. You blew it on Euler 735. You gave me INCORRECT
mathematical information then pulled your usual 3rd-grader "My stuff
ALWAYS works." when I proved you wrong.

> Fuck that "Project Euler." It's only for asshole string manipulators using
> bullshit Python.

First it's a "baloney" website.

Then it's a "well respected forum for programmers"

Then it's for "asshole string manipulators"

Which is which, twerp?

Le 09-03-2024, DFS <nospam@dfs.com> a écrit :
> On 3/9/2024 3:14 PM, Larry "The Prick" Piet wrote:
>
>> I am *ALWAYS* right. ALWAYS.
>
> You're a lying joke.

I'm not that sure about it. For the joke part, yes, of course, you are
right. But for the lying part it's a little more difficult to know. To
lie, you have to know the truth to be able to know you don't tell it.
But, as he's probably to stupid to know the truth, he's probably to
stupid to know if he's right or not. He pretend he is but it's probably
more for a comfort than for a strait lie.

>> Fuck that "Project Euler." It's only for asshole string manipulators using
>> bullshit Python.
>
> First it's a "baloney" website.
> Then it's a "well respected forum for programmers"
> Then it's for "asshole string manipulators"
>
> Which is which, twerp?

As I said, he probably has no clue. He can't answer honestly because he
just doesn't know.

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On 3/9/2024 2:14 PM, Diego Garcia wrote:
> Ain't no fucking picayune bullshit website gonna tell*ME* if I am right.

Hmm... picayune is a southerner term. I thought you were from up there
in north or northeast somewhere.

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On Sat, 9 Mar 2024 14:42:56 -0600, Physfitfreak wrote:

>
> I wish there was a chart I could look up, giving denominator integers
> (with prime factors other than 2 and 5) as its x axis and max number of
> repeating decimals as the y axis. With x interval going to about a
> million or even a billion.
>

Here are plots of the ranges 0-1000 and 0-10000:

https://i.postimg.cc/gkkGbtZj/prob26-1k.png

https://i.postimg.cc/0PxQCcrL/prob26-10k.png

You will need to download these images to view them in an off-line
image viewer that will allow scrolling.

The second image is 10000x1200 resolution and cannot fit within any
monitor.

There is a linear increase across the range. This is expected
because the Euler totient, which is directly related to the
repeat length, for a prime number p = p - 1.

Thus there will never be a repeat length of greater magnitude
than the number itself.

On 3/10/2024 1:55 AM, Farley Flud wrote:
> On Sat, 9 Mar 2024 14:42:56 -0600, Physfitfreak wrote:
>
>>
>> I wish there was a chart I could look up, giving denominator integers
>> (with prime factors other than 2 and 5) as its x axis and max number of
>> repeating decimals as the y axis. With x interval going to about a
>> million or even a billion.
>>
>
> Here are plots of the ranges 0-1000 and 0-10000:
>
> https://i.postimg.cc/gkkGbtZj/prob26-1k.png
>
> https://i.postimg.cc/0PxQCcrL/prob26-10k.png
>
> You will need to download these images to view them in an off-line
> image viewer that will allow scrolling.
>
> The second image is 10000x1200 resolution and cannot fit within any
> monitor.
>
> There is a linear increase across the range. This is expected
> because the Euler totient, which is directly related to the
> repeat length, for a prime number p = p - 1.
>
> Thus there will never be a repeat length of greater magnitude
> than the number itself.
>

The second image is also 0 to 1000, not 10000.

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On Sun, 10 Mar 2024 13:46:06 -0500, Physfitfreak wrote:

>
> The second image is also 0 to 1000, not 10000.
>

I'll have to fix this. In my haste I may have mixed up
the data files.

But the trend is the same as seen in the first plot, and it
will be same for plots up to a million or a billion and beyond.

On Sun, 10 Mar 2024 13:46:06 -0500, Physfitfreak wrote:

>
> The second image is also 0 to 1000, not 10000.
>

The second image is now corrected:

https://i.postimg.cc/FmKpsHzY/prob26-10k.png

Again, the resolution is 10000x1200 and it should be downloaded
and viewed off-line.

There is a clear upward, seemingly linear trend and this will
undoubtedly continue to infinity.

The educational system only describes repeating decimals
briefly because an in-depth analysis is beyond its resources.

But now we have CAS and we can examine repeating decimals
with ease.

Maxima can calculate this series up to a billion or more,
but it would take some time. I need to check out Pari,
which is a C program, and thus much faster:

https://pari.math.u-bordeaux.fr/

The relevant Pari function would be znorder(x, {o}):

https://pari.math.u-bordeaux.fr/dochtml/html/Arithmetic_functions.html

On Mon, 11 Mar 2024 08:40:32 +0000, Farley Flud wrote:

>
> Maxima can calculate this series up to a billion or more,
> but it would take some time. I need to check out Pari,
> which is a C program, and thus much faster:
>
> https://pari.math.u-bordeaux.fr/
>

I just checked pari. It is weird junk. C code has to be
written in a bizarre manner with their own garbage collection
functions. As a result, there is a somewhat steep learning curve.

Ialso looked at FLINT:

https://flintlib.org/

But FLINT does not have the functions I require.

I have settled on the Perl module Math::Prime::Util::GMP:

https://manpages.org/mathprimeutilgmp/3

This seems promising. For one thing, the input/output
is much easier to control with Perl than with Maxima.

FOSS is the greatest. Who would ever use Microslop?

On 3/11/2024 3:40 AM, Farley Flud wrote:
> On Sun, 10 Mar 2024 13:46:06 -0500, Physfitfreak wrote:
>
>>
>> The second image is also 0 to 1000, not 10000.
>>
>
> The second image is now corrected:
>
> https://i.postimg.cc/FmKpsHzY/prob26-10k.png
>
> Again, the resolution is 10000x1200 and it should be downloaded
> and viewed off-line.
>
> There is a clear upward, seemingly linear trend and this will
> undoubtedly continue to infinity.
>
> The educational system only describes repeating decimals
> briefly because an in-depth analysis is beyond its resources.
>
> But now we have CAS and we can examine repeating decimals
> with ease.
>
> Maxima can calculate this series up to a billion or more,
> but it would take some time. I need to check out Pari,
> which is a C program, and thus much faster:
>
> https://pari.math.u-bordeaux.fr/
>
> The relevant Pari function would be znorder(x, {o}):
>
> https://pari.math.u-bordeaux.fr/dochtml/html/Arithmetic_functions.html
>

Now 4 distinct trends can be discerned, with 4 different slopes. I can
only guess right now, but it may have something to do with the fact that
from 1 to 9 as denominator, there are four cases of repeated decimals
(3's, 6's, 142857's and 1's).

What are larger integer intervals anyway. They're like the 1 to 9
interval, only magnified to show higher resolutions, allowing more
numbers in between 1 and 9 to be treated as integers. This might be the
reason behind those 4 trends.

And if that's the case, then the same plot, but for 1 to 100000 or
higher interval, should still show only 4 trends, and not more.

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On Mon, 11 Mar 2024 16:17:08 -0500, Physfitfreak wrote:

>
> Now 4 distinct trends can be discerned, with 4 different slopes. I can
> only guess right now, but it may have something to do with the fact that
> from 1 to 9 as denominator, there are four cases of repeated decimals
> (3's, 6's, 142857's and 1's).
>

I don't know. This is my first foray into number theory.

I also have to shuffle this project between my current job and
housework, etc.

Just read the links I gave in my first post and they will provide
background.