Question

X 4 -y 4 = 15 , x and y are positive integers then x 4 + y 4 is

Answer 1

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I'm trying to find all the integer solutions for x4−y4=15x−y=. I know that the options are x2−y2=5,x2+y2=3x−y=x+y=, or x2−y2=1,x2+y2=15x−y=x+y=, or x2−y2=15,x2+y2=1x−y=x+y=, and the last one x2−y2=3,x2+y2=5x−y=x+y=.

Only the last one is valid. x2+y2=15x+y= is not solvable since the primes which have residue 33 modulo 44 is not of an equal power.

One particular solution for x2−y2=3,x2+y2=5x−y=x+y=, is x0=2,yo=1x=y=. How do I get to an expression of a general solution for this system?

Thanks!

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