28 Aug 2013

IrMO 1995 P2 Q5: Upper Secondary Mathematics Competition Question

For each integer n such that n = p1p2p3p4, where p1, p2, p3, p4 are distinct primes, let

d1 = 1 < d2 < d3 < ... < d15 < d16 = n

be the sixteen positive integers that divide n.
Prove that if n < 1995, then d9 - d8 ≠ 22.

[IrMO 1995 Paper 2 Question 5]

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