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p divides 2^{q-1}-1 and q divides 2^{p-1}-1

Source: Romania TST 7 2009, Problem 3

May 5, 2012
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Problem Statement

Show that there are infinitely many pairs of prime numbers (p,q)(p,q) such that p∣2q−1−1p\mid 2^{q-1}-1 and q∣2p−1−1q\mid 2^{p-1}-1.
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