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p is an odd prime congruent to 2 mod 3

Source: Balkan MO 1999, Problem 2

April 24, 2006
number theory proposednumber theory

Problem Statement

Let pp be an odd prime congruent to 2 modulo 3. Prove that at most p−1p-1 members of the set {m2−n3−1∣0<m, n<p}\{m^2 - n^3 - 1 \mid 0 < m,\ n < p\} are divisible by pp.
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