## Equation: a^4 + b^4 ± k = c^2

$a^4 \; + \; b^4 \; \pm \; k \; = \; c^2$

where   k   is a small odd integer.

k = +3

$2^4 \; + \; 3^4 \; + \; 3 \; = \; 10^2$
$116^4 \; + \; 825^4 + \; 3 \; = \; 680758^2$

k = -7

$2^4 \; + \; 2^4 \; - \; 7 \; = \; 5^2$
$14^4 \; + \; 80^4 \; - \; 7 \; = \; 6403^2$

k = +7

$3^4 \; + \; 3^4 \; + \; 7 \; = \; 13^2$

Find other solutions where k is a small odd integer.