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Primes and square-free integers

Source: Bulgarian IMO TST 2004, Day 1, Problem 2

July 8, 2013
floor functionnumber theory proposednumber theory

Problem Statement

Find all primes p≥3p \ge 3 such that p−⌊p/q⌋qp- \lfloor p/q \rfloor q is a square-free integer for any prime q<pq<p.
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