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).
Finch, S. "On a Generalized Fermat-Wiles Equation." http://algo.inria.fr/csolve/fermat.pdf.Sloane,
N. J. A. Sequence A001481/M0968
in "The On-Line Encyclopedia of Integer Sequences."
,
,
,
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).
