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b is perfect square when b^2 = a^2 + ab + b

Source: 2020 Czech and Slovak Olympiad III A p4

November 24, 2020
number theoryPerfect Square

Problem Statement

Positive integers a,ba, b satisfy equality b2=a2+ab+bb^2 = a^2 + ab + b. Prove that bb is a square of a positive integer.
(Patrik Bak)
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