## a^4 + 4*b^4 = c^4 + 4*d^4

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

$a, b, c, d$   are distinct integers,    and    $a \; \leq \; 10,000$

$8^4 \; + \; 4(9)^4 \; = \; 12^4 \; + \; 4(7)^4 \; = \; 30340$

$36^4 \; + \; 4(16)^4 \; = \; 28^4 \; + \; 4(24)^4 \; = \; 1941760$
$92^4 \; + \; 4(19)^4 \; = \; 64^4 \; + \; 4(61)^4 \; = \; 72160580$

$188^4 \; + \; 4(12)^4 \; = \; 132^4 \; + \; 4(124)^4 \; = \; 1249281280$
$336^4 \; + \; 4(11)^4 \; = \; 244^4 \; + \; 4(219)^4 \; = \; 12745565380$
$548^4 \; + \; 4(56)^4 \; = \; 412^4 \; + \; 4(352)^4 \; = \; 90221830400$
$836^4 \; + \; 4(129)^4 \; = \; 648^4 \; + \; 4(529)^4 \; = \; 489563310340$

$1212^4 \; + \; 4(236)^4 \; = \; 964^4 \; + \; 4(756)^4 \; = \; 2170204652800$
$1688^4 \; + \; 4(383)^4 \; = \; 1372^4 \; + \; 4(1039)^4 \; = \; 8204831881220$
$2276^4 \; + \; 4(576)^4 \; = \; 1884^4 \; + \; 4(1384)^4 \; = \; 27274524647680$
$2988^4 \; + \; 4(821)^4 \; = \; 2512^4 \; + \; 4(1797)^4 \; = \; 81529080363460$
$3836^4 \; + \; 4(1124)^4 \; = \; 3268^4 \; + \; 4(2284)^4 \; = \; 222912639960320$
$4832^4 \; + \; 4(1491)^4 \; = \; 4164^4 \; + \; 4(2851)^4 \; = \; 564907920484420$
$5988^4 \; + \; 4(1928)^4 \; = \; 5212^4 \; + \; 4(3504)^4 \; = \; 1340932890108160$
$7316^4 \; + \; 4(2441)^4 \; = \; 6424^4 \; + \; 4(4249)^4 \; = \; 3006817144418180$
$8828^4 \; + \; 4(3036)^4 \; = \; 7812^4 \; + \; 4(5092)^4 \; = \; 6413477697291520$