Modularistics!

We usually find the remainder of a x a^x when divided by some integers with a a for some integers and x x for some natural numbers. IA would be mad if I don't share this problem.

Find the minimum value of x , x N x, x\in \mathbb{N} which satisfies the mod equations below!

6 0 x 0 ( m o d 10368 ) 60^{x} \equiv 0 (\mod{10368})


The answer is 4.

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