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

Home > Numbers
Further Arithmetic Integers (Posted on 2006-06-27) Difficulty: 3 of 5
Consider three positive integers x < y < z in arithmetic sequence, and determine all possible solutions of: x4 + y4 = z4 - 64

See The Solution Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
mathematica solution (spoiler) | Comment 5 of 10 |
gotta love mathematica's reduce function

Fnc[x_,y_]:=15*y^4-32*x*y^3+24*x^2*y^2-8*x^3*y-64;
Reduce[{Fnc[x,y]==0,y>x,x>0},{x,y},Integers]

how I got the Fnc function is I used z=y+(y-x)=2y-x and set all equal to zero

in a matter of miliseconds it pops out

x=1,y=2
x=7,y=8

  Posted by Daniel on 2006-06-28 06:03:32
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (1)
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 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information