Permutations/ Same Sequence Of Signs As Inverses

[Richard Mathar]

>SeqFans,
>
>is there a chance to find more solutions to
>
>x^4 + y^4 = c * z^4 with c > 1 and gcd(x,y,z)=1

of course also z > 1, because otherwise all solutions of A003336 would be included.

The only known solution matching the criteria is 25^4 + 149^4 = 5906*17^4

If someone wants to go for larger exponents then find more of the kind
15^5 + 17^5 = 68101*2^5 (typo "2*5" in original message)

Hugo