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 $N$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "Let N be the number of ordered triples (A,B,C) of integers satisfying the conditions
a) 0\\leq A<B<C\\leq99,
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.
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.
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