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Trivial NT in TST

Source: Netherlands TST for IMO 2017,day 2 problem 1

February 1, 2018
number theory

Problem Statement

Let a,b,ca, b,c be distinct positive integers, and suppose that p=ab+bc+cap = ab+bc+ca is a prime number. (a)(a) Show that a2,b,c2a^2,b^,c^2 give distinct remainders after division by pp. (b) Show that a3,b3,c3a^3,b^3,c^3 give distinct remainders after division by pp.
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