## Diophantine Eq. : a^2 + b^2 + c^2 = 2d^2 and a^4 + b^4 + c^4 = 2d^4

Determine all integral solutions of the simultaneous Diophantine equations:

$a^2 \; + \; b^2 \; + \; c^2 \; = \; 2 \, d^2$
$a^4 \; + \; b^4 \; + \; c^4 \; = \; 2 \, d^4$