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a,b,c positive integers, a^2 + b^2 + 1 = c^2, prove [a/2] + [c / 2] is even

Source: Rioplatense Olympiad 2000 level 3 P4

September 6, 2018
number theorypositive integersInteger PartEven

Problem Statement

Let a,ba, b and cc be positive integers such that a2+b2+1=c2a^2 + b^2 + 1 = c^2 . Prove that [a/2]+[c/2][a/2] + [c / 2] is even.
Note: [x][x] is the integer part of xx.
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