Aritmethic Pythagorean Triples

Number Theory Level 2

Dan claims that in every arithmetic progression of non-negative integers in which the first element is 0, there exist three integer numbers a , b a,b and c c such that a 2 + b 2 = c 2 { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 } . Is Dan's claim true?

No Yes

Mateo Matijasevick by Mateo Matijasevick , 22, Colombia

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1 solution

Jon Mills
Oct 19, 2017

If n is the first number of the progression then by definition 3n, 4n and 5n will also be in there and these 3 numbers are always a Pythagorean Triple

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