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p = kq + r and a^2 | r

Source: China TST 1999, problem 2

May 22, 2005
number theoryprime numbersnumber theory unsolved

Problem Statement

Find all prime numbers pp which satisfy the following condition: For any prime q<pq < p, if p=kq+r,0≤r<qp = kq + r, 0 \leq r < q, there does not exist an integer q>1q > 1 such that a2∣ra^{2} \mid r.
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