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2020 OIM Problems/Problem 2

Problem

For each positive integer $n$, define $T_n$ as the smallest positive integer such that $1 + 2 + \cdots + T_n$ is a multiple of $n$. For example, $T_5 = 4$ since $1$, $1 + 2$ and $1 + 2 + 3$ are not multiples of $5$, but $1 + 2 + 3 + 4$ is a multiple of $5$. Find all positive integers $m$ such that $T_m \ge m$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions

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