2014 Canadian MO Problems/Problem 3

Problem

Let $p$ be a fixed odd prime. A $p$ -tuple $(a_1,a_2,a_3,\ldots,a_p)$ of integers is said to be good if

(i) $0\le a_i\le p-1$ for all $I$ , and (ii) $a_1+a_2+a_3+\cdots+a_p$ is not divisible by $p$ , and (iii) $a_1a_2+a_2a_3+a_3a_4+\cdots+a_pa_1$ is divisible by $p$ .

Determine the number of good $p$ -tuples.

Solution

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2014 Canadian MO Problems/Problem 3

Problem

Solution