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MEMO 2010, Problem I-4: Difference of divisors divides n

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September 11, 2010
inequalitiesnumber theory proposednumber theoryeasy problem

Problem Statement

Find all positive integers nn which satisfy the following tow conditions: (a) nn has at least four different positive divisors; (b) for any divisors aa and bb of nn satisfying 1<a<b<n1<a<b<n, the number bāˆ’ab-a divides nn.
(4th Middle European Mathematical Olympiad, Individual Competition, Problem 4)
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