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1/2 (c - a) (c - b) is perfect square for positive integers such a^2 + b^2 = c^2

Source: Czech-Polish-Slovak Junior Match 2012, Individual p5 CPSJ

March 11, 2020
number theoryPythagorean TriplePerfect Square

Problem Statement

Positive integers a,b,ca, b, c satisfying the equality a2+b2=c2a^2 + b^2 = c^2. Show that the number 12(c−a)(c−b)\frac12(c - a) (c - b) is square of an integer.
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