Answer:
for integer
(including negative numbers.)
Explanation:
Pythagorean Identity:
. Equivalently,
.
Rewrite the original equation and apply this substitution to eliminate
:
.
.
.
Let
(
.) The original equation is equivalent to the following equation about
:
.
Expand the cubic binomial in the equation:
.
.
Simplify to obtain:
.
Rearrange and simplify:
.
.
.
.
Solve for
:
Either
or
.
If
, then
for all
.
On the other hand, if
, then
for all
.
Combine both situations to obtain:
for all
.