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Cono Sur Olympiad 2013, Problem 5

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August 22, 2014
number theory proposednumber theory

Problem Statement

Let d(k)d(k) be the number of positive divisors of integer kk. A number nn is called balanced if d(n−1)≤d(n)≤d(n+1)d(n-1) \leq d(n) \leq d(n+1) or d(n−1)≥d(n)≥d(n+1)d(n-1) \geq d(n) \geq d(n+1). Show that there are infinitely many balanced numbers.
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