IZhO 2013, Олимпиада по математика · първи ден — Задача 2

IX International Zhautykov Olympiad in Mathematics, Almaty, 2013, 15 January, 2013, 9.00–13.30, First day · 15 януари 2013 г. · 7 т.

Условие

Find all odd positive integers $n > 1$ such that there is a permutation $a_1, a_2, ..., a_n$ 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 $k, 1 \le k \le n$ (we assume $a_{n+1} = a_1$).

Решение

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Оригинал в Архива: IZhO_2013_1day- mathem.doc