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

Home > Numbers
No software allowed ! (Posted on 2017-05-07) Difficulty: 3 of 5
Find positive integers a, b, and c, all different, such that
a^3 + b^3 = c^4.

Please obey the title !

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 6
Let x,y,z be any set of positive integer satisfying z=x^3+y^3.  Then c=z, a=x*z, b=y*z is an integral solution to a^3 + b^3 = c^4.

For example, 2^3+3^3=35 makes (x,y,z)=(2,3,35) Then (a,b,c)=(70,105,35) yields 70^3+105^3=35^4=1500625.

  Posted by Brian Smith on 2017-05-07 10:09:40
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information