All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 (7N-1 – 1)/N = Perfect Square (Posted on 2010-04-24)
Determine all possible prime number(s) N such that (7N-1 – 1)/N is a positive perfect square.

Prove that these are the only value(s) of N that satisfy the given conditions.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer exploration Comment 1 of 1

The only prime under 3049 that works is 3. The following program checks up to that value, when the value of (7^(N-1)-1)/N becomes a 2573-digit number, preventing UBASIC from taking its square root via built-in function.

`list    5   N=1   10   while N>0   20     N=nxtprm(N)   30     V=(7^(N-1)-1)//N   40     if V=int(V) then   50        :Sr=int(sqrt(V)+0.5)   60        :if Sr*Sr=V then print N;V;Sr   70   wendOKrun 3  16  4Overflow in 50?n,v 3049    23695645235380467868868309285488693124310463191804539500437171340734782748096223591770416265973039278259279932290362940938756891440125190913313366587411809100809398799409988159682794587500482156359795580540625873070663910307056855899995024113449304679655735987985420907852768321429628485903406058488842208955767742316034773347800797755135505125615809482403171114759842231064572077883761651689471100630080522571388800905072311572227985254399755397838096879972812009181305776643490295506732856571386249648360680072483583587029283396053844872106083467116362881012857760895502442204628590191701859774265483867871120867444019731173722398405552636003778499499931870152750401313308054461185220621054017257779940926470848968034290001380993744265710162584674144841700891858545722327384299273526734543083789699078842401093866797041126164943615415289938268891109120458953422048458327332284106583628406853336713621373122691811183752187537966675340073148105363009934966132565094933473574742805783016045702459997258641642471734070164136737486860332800555858135426615450249949126735233711096919050258143241122171079789441679525495378038042222355445739144706913000077770470724625475461647141998990925475707107285402262763454934713802961031468762887546763130515770967804076810001433192934357723436042341567876085308628841956405229232312242408075874714767382555088013814613585055795479428431622475551197452930167830899516667732362149605352431427928278927454899408107081566627217075485133981729223704622081180446238137628932340358479418186960529232912860046582178430567766459751472751005184178597467217042988986669099736394823070188811962711966876810564767873671069471534518507465905665949428090489233028236733040453074313546378659213308452417161517215338326297092625872668314728418210050056134465657942207533970732700333837355768038027070403740861437228594629041378626508538074046518637638247293806407146674198364527127366591046556189294829319989357029462824789420057963766947272303385892804459978821730671419398891965033918098251686977439593223428662939685155092923937238135854866362222859010890617266758185799864893162548134122865686880647914530713403272999326789171168733166193338391759197160741747798605501343548346605909714994158464842241189128063366130467208772828421097690130717161946936868766584679905673099075718801863514261482930974773148786577425388629671533016859828801783772071355473997233401951240657767146248282621194914625997802990821948697492046445753119771111246057032699202505849747642910246670408420601981503724592963500565816341179969299660396318830706207847410180171200OK`

 Posted by Charlie on 2010-04-24 13:43:39

 Search: Search body:
Forums (0)