Generalized Fermat Equation

A generalization of the equation whose solution is desired in Fermat's last theorem

to

for , , , and  positive constants, with trivial solutions having , , or  being excluded.

 is trivial to solve by taking  and .  is more difficult, but can be solved by noting that solutions exist for values of  which can be written as a sum of two squares, the first few of which are 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, ... (OEIS A001481).

REFERENCES:

Finch, S. "On a Generalized Fermat-Wiles Equation." https://algo.inria.fr/csolve/fermat.pdf.

Sloane, N. J. A. Sequence A001481/M0968 in "The On-Line Encyclopedia of Integer Sequences."