<s>[INST] On the equation $a^4+b^4+c^4=2d^4$ in positive integers $a\lt b\lt c$ such that $a+b\ne c$ Background: The equation
$$a^4+b^4+c^4=2d^4$$
has infinitely many positive integral solutions if we take $c=a+b$ and $a^2+ab+b^2=d^2$ further assuming that $GCD(a,b,c)=1$.
Main problem: Find some positive integral solutions to the equation
$$a^4+b^4+c^4=2d^4$$
with $a\lt b\lt c\ne a+b$ and $GCD(a,b,c)=1$.
 [/INST] $(a, b, c, d) = (32, 1065, 2321, 1973), (2156, 5605, 8381, 7383)$
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