Consider three positive integers x < y < z in arithmetic sequence, and determine all possible solutions of:
x^{4} + y^{4} = z^{4}  64
gotta love mathematica's reduce function
Fnc[x_,y_]:=15*y^432*x*y^3+24*x^2*y^28*x^3*y64;
Reduce[{Fnc[x,y]==0,y>x,x>0},{x,y},Integers]
how I got the Fnc function is I used z=y+(yx)=2yx 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 20060628 06:03:32 