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 \(\left | AC - B \right |\).
by
Steven Yuan