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p | n^2 -n+3 iff p | m^2 -m+25

Source: Polish second round 1994 p6

January 19, 2020
number theorydividesprime

Problem Statement

Let pp be a prime number. Prove that there exists n∈Zn \in Z such that p∣n2−n+3p | n^2 -n+3 if and only if there exists m∈Zm \in Z such that p∣m2−m+25p | m^2 -m+25.
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