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Least integer T_m such that m divides gauss sum

Source: 2020 Iberoamerican P2

November 17, 2020
number theoryIberoamerican

Problem Statement

Let TnT_n denotes the least natural such that n∣1+2+3+⋯+Tn=∑i=1Tnin\mid 1+2+3+\cdots +T_n=\sum_{i=1}^{T_n} i Find all naturals mm such that m≥Tmm\ge T_m.
Proposed by Nicolás De la Hoz
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