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Infinitely many integers n with d(n!)-1 a composite number

Source: China TST 2011 - Quiz 2 - D1 - P3

March 24, 2011
number theoryIMO Shortlistnumber theory unsolved

Problem Statement

For any positive integer dd, prove there are infinitely many positive integers nn such that d(n!)āˆ’1d(n!)-1 is a composite number.
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