Find all of the Pythagorean triples that consist of consecutive positive integers. Prove that you have found them all.

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- November 1st 2010, 05:18 PMMATNTRNGPythagorean Triples
Find all of the Pythagorean triples that consist of consecutive positive integers. Prove that you have found them all.

- November 1st 2010, 09:02 PMSoroban
Hello, MATNTRNG!

Quote:

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: .