Iran 2015, TST2, D2, P2

For discussing Olympiad Level Number Theory problems
tanmoy
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Iran 2015, TST2, D2, P2

Unread post by tanmoy » Wed Dec 28, 2016 7:11 pm

We call a permutation $(a_1, a_2,\cdots , a_n)$ of the set $\{ 1,2,\cdots, n\}$ "good" if for any three natural numbers $i <j <k$, $n\nmid a_i+a_k-2a_j$. Find all natural numbers $n\ge 3$ such that there exists a "good" permutation of a set $\{1,2,\cdots, n\}.$
"Questions we can't answer are far better than answers we can't question"

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