## 2013 AIME I Problem 15

2013 AIME I 15. Let $N$ be the number of ordered triples $(A, B, C)$ of integers satisfying the conditions

(a) $0 \leq A < B < C \leq 99$,
(b) there exist integers $a$, $b$, and $c$, and prime $p$ where $0 \leq b < a < c < p$,
(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 $N$.