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a+1 is perfect square if a^2+a = 3b^2

Source: Polish MO second round 1966 p4

August 28, 2024
number theoryPerfect Square

Problem Statement

Prove that if the natural numbers a a and b b satisfy the equation a2+a=3b2 a^2+a = 3b^2 , then the number a+1 a+1 is the square of an integer.
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