Hello, MATNTRNG!

Find all of the Pythagorean triples that consist of consecutive positive integers.

Prove that you have found them all.

Let the triple be: .

Then we have: .

. . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

Since is a positive integer,

Therefore, the only Pythagorean triple is: .