Finding all integral solutions of $x^4+y^4+z^4-w^4=1995$ Find all the integral solutions of 
$$x^4+y^4+z^4-w^4=1995.$$
Please elaborate the solution. I tried but can't understand what to do.

Fourth powers are either of $$ 0,1 \pmod {16}. $$ The possibilities are
$$  x^4 + y^4 + z^4 - w^4 \equiv 15,0,1,2,3 \pmod {16}.  $$ However,
$$  1995 \equiv 11 \pmod {16}.  $$
