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no of pos. integers n suh that p | n! +1 is <= cp^{2/3}

Source: Ukraine TST 2014 p12

April 30, 2020
primenumber theoryDivisibility

Problem Statement

Prove that for an arbitrary prime p≥3p \ge 3 the number of positive integers nn, for which p∣n!+1p | n! +1 does not exceed cp2/3cp^{2/3}, where c is a constant that does not depend on pp.
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