2013 AIME I Problem 15

Let N be the number of ordered triples (A,B,C) of integers satisfying the conditions:

(a) 0\le A<B<C\le99,

(b) there exist integers a, b, and c, and prime p where 0\le b<a<c<p,

(c) p divides A-a, B-b, and C-c, and

(d) each ordered triple (A,B,C) and each ordered triple (b,a,c) form arithmetic sequences. Find N.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.