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Two equations with result a = bc.

Source: Kazakhstan National Olympiad 2024 (9 grade), P1

March 21, 2024
algebranumber theory

Problem Statement

Positive integers a,b,ca,b,c satisfy the equations a2=b3+aba^2=b^3+ab and c3=a+b+cc^3=a+b+c. Prove that a=bca=bc.
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