MathDB
Polish MO Finals 2018, Problem 4

Source:

April 19, 2018
number theoryPolandTST

Problem Statement

Let nn be a positive integer. Suppose there are exactly MM squarefree integers kk such that ⌊nk⌋\left\lfloor\frac nk\right\rfloor is odd in the set {1,2,…,n}\{ 1, 2,\ldots, n\}. Prove MM is odd.
An integer is squarefree if it is not divisible by any square other than 11.
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