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Omni-MATH / Determine all integers n≥2 such that there exists a permutation x₀,x₁,…,x_(n−1) of the numbers 0,1,…,n−1 with the property that the n numbers …

Problem

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problem

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 $$x_0, \hspace{0.3cm} x_0 + x_1, \hspace{0.3cm} \ldots, \hspace{0.3cm} x_0 + x_1 + \ldots + x_{n - 1}$$ are pairwise distinct modulo nn.
Plain-text mathematical notation (without MathML)
Determine all integers n≥2 such that there exists a permutation x₀,x₁,…,x_(n−1) of the numbers 0,1,…,n−1 with the property that the n numbers
$$x_0, \hspace{0.3cm} x_0 + x_1, \hspace{0.3cm} \ldots, \hspace{0.3cm} x_0 + x_1 + \ldots  + x_{n - 1}$$
are pairwise distinct modulo n.
Original LaTeX notation
Determine all integers $n \geq 2$ such that there exists a permutation $x_0, x_1, \ldots, x_{n - 1}$ of the numbers $0, 1, \ldots, n - 1$ with the property that the $n$ numbers
$$x_0, \hspace{0.3cm} x_0 + x_1, \hspace{0.3cm} \ldots, \hspace{0.3cm} x_0 + x_1 + \ldots  + x_{n - 1}$$
are pairwise distinct modulo $n$.

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Source and history

task_id
50079179-6b9e-5b7e-9e61-9a31810aa792
task_key
test--50079179-6b9e-5b7e-9e61-9a31810aa792
task_revision_id
1
config / split
/ test

Official source

initial import