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Square-free residues

Source: Bulgarian TST's 2004 --- Problem 2.

May 27, 2004
floor functionnumber theory solvednumber theory

Problem Statement

Find all primes p≥3p \geq 3 with the following property: for any prime q<pq<p, the number p−⌊pq⌋q p - \Big\lfloor \frac{p}{q} \Big\rfloor q is squarefree (i.e. is not divisible by the square of a prime).
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