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2013 ToT Fall Senior O p3 [n, n + 1] > [n, n + 2] >...> [n, n + 35], lcm

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March 22, 2020
LCMnumber theoryinequalitiesleast common multiple

Problem Statement

Denote by [a,b][a, b] the least common multiple of aa and bb. Let nn be a positive integer such that [n,n+1]>[n,n+2]>...>[n,n+35][n, n + 1] > [n, n + 2] >...> [n, n + 35]. Prove that [n,n+35]>[n,n+36][n, n + 35] > [n,n + 36].
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