wu :: forums
wu :: forums - Coprime Cubes

Welcome, Guest. Please Login or Register.
Jan 23rd, 2022, 3:38am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: Grimbal, Eigenray, Icarus, ThudnBlunder, william wu, SMQ, towr)
   Coprime Cubes
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Coprime Cubes  (Read 1503 times)
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
*****




The dewdrop slides into the shining Sea

   


Gender: male
Posts: 4489
Coprime Cubes  
« on: Jul 4th, 2008, 6:39am »
Quote Quote Modify Modify

Find the smallest solution to a3/b3 + c3/d3 = 6
where a,b,c,d are coprime positive integers > 100, not necessarily distinct.  
IP Logged

THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Coprime Cubes  
« Reply #1 on: Jul 4th, 2008, 6:58am »
Quote Quote Modify Modify

on Jul 4th, 2008, 6:39am, ThudanBlunder wrote:
where a,b,c,d are coprime positive integers > 100, not necessarily distinct.
If they're coprime, and >100, then I'd say they're necessarily distinct.
Or do you mean something other than pairwise coprime? i.e. gcd(a,b)=gcd(a,c)=gcd(a,d)=gcd(b,c)=gcd(b,d)=gcd(c,d)=1 ?
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
*****




The dewdrop slides into the shining Sea

   


Gender: male
Posts: 4489
Re: Coprime Cubes  
« Reply #2 on: Jul 4th, 2008, 7:21am »
Quote Quote Modify Modify

OK, 2 of the required integers are equal. Hence consider the 3 distinct integers a,b,c to be coprime.
IP Logged

THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
Barukh
Uberpuzzler
*****






   


Gender: male
Posts: 2276
Re: Coprime Cubes  
« Reply #3 on: Jul 4th, 2008, 11:06am »
Quote Quote Modify Modify

This is relevant.
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright 2000-2004 Yet another Bulletin Board