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Find smallest positive integer

Source: China Western Mathematical Olympiad 2012 P1

September 29, 2012
modular arithmeticnumber theoryprime numbersnumber theory proposed

Problem Statement

Find the smallest positive integer mm satisfying the following condition: for all prime numbers pp such that p>3p>3,have 105∣9p2−29p+m.105|9^{ p^2}-29^p+m. (September 28, 2012, Hohhot)
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