From: Diego Garcia <dg@chaos.rocks>
Subject: Re: Project Euclid Problem 26 SOLVED!!!
Newsgroups: comp.os.linux.advocacy
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Date: Sat, 09 Mar 2024 20:01:08 +0000
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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):

0.0010172939979654120040691759918616480162767039674465920651068158697863682604272634791454730417090539165818921668362156663275686673448626653102746693794506612410986775178026449643947100712105798575788402848423194303153611393692777212614445574771108850457782299084435401831129196337741607324516785350966429298067141403865717192268565615462868769074262461851475076297049847405900305188199389623601220752797558494404883011190233977619532044760935910478128179043743641912512716174974567650050864699898270600203458799593082400813835198372329603255340793489318413021363173957273652085452695829094608341810783316378433367243133265513733468972533062054933875890132248219735503560528992878942014242115971515768056968463886063072227873855544252288911495422177009155645981688708036622583926754832146490335707019328585961342828077314343845371312309257375381485249237029501525940996948118006103763987792472024415055951169888097660223804679552390640895218718209562563580874872838250254323499491353001017293997965412004069175991861648016276703967446592065106815869786368260427263479145473041709053916581892166836215666327568667344862665310274669379450661241098677517802644964394710071210579857578840284842319430315361139369277721261444557477110885045778229908443540183112919633774160732451678535096642929806714140386571719226856561546286876907426246185147507629704984740590030518819938962360122075279755849440488301119023397761953204476093591047812817904374364191251271617497456765005086469989827060020345879959308240081383519837232960325534079348931841302136317395727365208545269582909460834181078331637843336724313326551373346897253306205493387589013224821973550356052899287894201424211597151576805696846388606307222787385554425228891149542217700915564598168870803662258392675483214649033570701932858596134282807731434384537131230925737538148524923702950152594099694811800610376398779247202441505595116988809766022380467955239064089521871820956256358087487283825025432349949135300101729399796541200406917599186164801627670396744659206510681586978636826042726347915