MathDB
lcm (n, n + 1, n + 2, ... , n + k) > lcm (n + 1, n + 2, n + 3,... , n + k + 1)

Source: 2010 Brazil IMO TST 3.2

July 24, 2021
number theoryleast common multipleLCM

Problem Statement

Let k>1k > 1 be a fixed integer. Prove that there are infinite positive integers nn such that lcm (n,n+1,n+2,...,n+k)>lcm (n+1,n+2,n+3,...,n+k+1). lcm \, (n, n + 1, n + 2, ... , n + k) > lcm \, (n + 1, n + 2, n + 3,... , n + k + 1).
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