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Partial sums are distinct modulo n

Source: MEMO 2017 T7

August 25, 2017
number theory

Problem Statement

Determine all integers n≥2n \geq 2 such that there exists a permutation x0,x1,…,xn−1x_0, x_1, \ldots, x_{n - 1} of the numbers 0,1,…,n−10, 1, \ldots, n - 1 with the property that the nn numbers x0,x0+x1,…,x0+x1+…+xn−1x_0, \hspace{0.3cm} x_0 + x_1, \hspace{0.3cm} \ldots, \hspace{0.3cm} x_0 + x_1 + \ldots + x_{n - 1} are pairwise distinct modulo nn.
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