wu :: forums « wu :: forums - Coprime Cubes » Welcome, Guest. Please Login or Register. Jan 23rd, 2022, 3:38am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    riddles    hard (Moderators: Grimbal, Eigenray, Icarus, ThudnBlunder, william wu, SMQ, towr)    Coprime Cubes « Previous topic | Next topic »
 Pages: 1 Reply Notify of replies Send Topic Print
 Author Topic: Coprime Cubes  (Read 1503 times)
ThudnBlunder
wu::riddles Moderator
Uberpuzzler

The dewdrop slides into the shining Sea

Gender:
Posts: 4489
 Coprime Cubes   « on: Jul 4th, 2008, 6:39am » Quote 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:
Posts: 13730
 Re: Coprime Cubes   « Reply #1 on: Jul 4th, 2008, 6:58am » Quote 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:
Posts: 4489
 Re: Coprime Cubes   « Reply #2 on: Jul 4th, 2008, 7:21am » Quote 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:
Posts: 2276
 Re: Coprime Cubes   « Reply #3 on: Jul 4th, 2008, 11:06am » Quote Modify

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

 Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium => hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »