Consider three positive integers x < y < z in arithmetic sequence, and determine all possible solutions of:
x4 + y4 = z4 - 64
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 |
mathematica solution (spoiler)
