All integer solutions for $x^4-y^4=15$ I'm trying to find all the integer solutions for $x^4-y^4=15$.
I know that the options are $x^2-y^2=5, x^2+y^2=3$, or $x^2-y^2=1, x^2+y^2=15$, or $x^2-y^2=15, x^2+y^2=1$, and the last one $x^2-y^2=3, x^2+y^2=5$. 
Only the last one is valid. $x^2+y^2=15$ is not solvable since the primes which have residue $3$ modulo $4$ is not of an equal power.
One particular solution for $x^2-y^2=3, x^2+y^2=5$, is $x_0=2, y_o=1$. How do I get to an expression of a general solution for this system?
Thanks!

$$(x^2-y^2)+(x^2+y^2)=2x^2=3+5=8\Rightarrow x^2=4\Rightarrow x=2,-2$$
$$(x^2+y^2)-(x^2-y^2)=2y^2=5-3=2\Rightarrow y^2=1\Rightarrow y=1,-1$$
Substitute the values to check that these are indeed the soloutions.
