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JBMO TST Bosnia and Herzegovina 2022 P2

Source: JBMO TST Bosnia and Herzegovina 2022

May 21, 2022
JBMO TSTnumber theorynational olympiad

Problem Statement

Let a,b,ca,b,c be positive integers greater than 11 such that p=ab+bc+acp=ab+bc+ac is prime. A) Prove that a2,b2,c2a^2, b^2, c^2 all have different reminder mod pmod\ p. B) Prove that a3,b3,c3a^3, b^3, c^3 all have different reminder mod pmod\ p.
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