iran-konkur 2021 Q135

iran-konkur · Other · konkur-riazi_1400_specialized Number Theory Modular Arithmetic Computation
135. If $m$ is the largest natural number such that $36 \equiv (m)! \pmod{15}$, then $m^{123}$ divided by $15$, the remainder is which of the following?
(1) $1$ (2) $2$ (3) $4$ (4) $6$
\textbf{135.} If $m$ is the largest natural number such that $36 \equiv (m)! \pmod{15}$, then $m^{123}$ divided by $15$, the remainder is which of the following?

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(1) $1$ \hfill (2) $2$ \hfill (3) $4$ \hfill (4) $6$

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