View source for 2014 Canadian MO Problems/Problem 3

== Problem ==
Let <math>p</math> be a fixed odd prime. A <math>p</math>-tuple <math>(a_1,a_2,a_3,\ldots,a_p)</math> of integers is said to be good if 

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

Determine the number of good <math>p</math>-tuples.     

==Solution==
{{Solution}}