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Omni-MATH / Find all odd positive integers n>1 such that there is a permutation a₁,a₂,…,a_(n) of the numbers 1,2,…,n, where n divides one of the numbers a_(k)²−a_(k+1)−1 and a_(k)²−a_(k+1)+1 f…

Problem

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problem

Find all odd positive integers n>1n>1 such that there is a permutation a1,a2,…,ana_{1}, a_{2}, \ldots, a_{n} of the numbers 1,2,…,n1,2, \ldots, n, where nn divides one of the numbers ak2−ak+1−1a_{k}^{2}-a_{k+1}-1 and ak2−ak+1+1a_{k}^{2}-a_{k+1}+1 for each k,1≤k≤nk, 1 \leq k \leq n (we assume an+1=a1a_{n+1}=a_{1} ).
Plain-text mathematical notation (without MathML)
Find all odd positive integers n>1 such that there is a permutation a₁,a₂,…,a_(n) of the numbers 1,2,…,n, where n divides one of the numbers a_(k)²−a_(k+1)−1 and a_(k)²−a_(k+1)+1 for each k,1≤k≤n (we assume a_(n+1)=a₁ ).
Original LaTeX notation
Find all odd positive integers $n>1$ such that there is a permutation $a_{1}, a_{2}, \ldots, a_{n}$ of the numbers $1,2, \ldots, n$, where $n$ divides one of the numbers $a_{k}^{2}-a_{k+1}-1$ and $a_{k}^{2}-a_{k+1}+1$ for each $k, 1 \leq k \leq n$ (we assume $a_{n+1}=a_{1}$ ).

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Source and history

task_id
d6b4b3b9-1a30-508f-a5f9-103c9132c929
task_key
test--d6b4b3b9-1a30-508f-a5f9-103c9132c929
task_revision_id
1
config / split
/ test

Official source

initial import