MathDB

Determine the number of "good" p-tuples

Source: 2014 CMO #3

May 11, 2014

number theory proposednumber theory

Problem Statement

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.

Back to Problems View on AoPS