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July 10

Pythagorean triples

In Pythagorean triples, it says "Every integer greater than 2 is part of a primitive or non-primitive Pythagorean triple, for example, the integers 6, 10, 14, and 18 are not part of primitive triples, but are part of the non-primitive triples 6, 8, 10; 14, 48, 50 and 18, 80, 82". How does one go about proving that?

I can get as far as proving that the "first integer not in the above set must be a prime". But then I get stuck. -- 84.12.125.33 (talk) 11:16, 10 July 2012 (UTC)[reply]

Let a be any odd number above 1. Choose m = n+1 in the first formula in Pythagorean triple#Generating a triple, and then choose n so a = m² - n². PrimeHunter (talk) 11:36, 10 July 2012 (UTC)[reply]