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A well-known conjecture asserts that there are infinitely many primes p for which p - 1 is a perfect square. We obtain upper and lower bounds of matching order on the number of pairs of distinct primes p,q < x for which (p - 1)(q - 1) is a perfect square.doi:10.1142/s179304211550102x fatcat:oivw3zblnfek3gel7iywiars7a