Hello, Alex!
Prove that there are infinitely many positive integers such that
can be expressed as a sum of two positive squares in at least two different ways.
(Here and are considered as the same representation.)
ThePerfectHacker hinted at an interesting identity,
. . one I had run across many years ago.
Let
. . and there are an infinite number of Pythagorean triples.
And we have: .
Let and we have: . which has the form:
Example: .use
. . . . . . . . . all equal to 650
Example: use
. . . . . . . . . all equal to 28,730