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.)
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