Euler is Everywhere! #1

Number Theory Level 5

Let \(A\) be the smallest positive integer such that \(1441^{1441} \equiv -A \pmod{2015}\).

Let \(B\) be the number of positive integer values of \(n\) such that \(n \leq 2014\) and the remainder when \(n^{936}\) is divided by \(2014\) is not \(1.\)

Let \(C = 1\) if \(123456789^{6000} \equiv 1 \pmod{2013},\) and \(C = 2\) if not.

Evaluate \(\left | AC - B \right |\).

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