What is the smallest positive N that will satisfy the following modular equation?

25,111^N mod 31 = 1. Thank you for help.

 Apr 7, 2018

Since the base of 25,111 itself mod 31 = 1, it, therefore, follows that any N from N=1 to infinity will always give a remainder of 1. So, the smallest positive integer is 1.

 Apr 7, 2018

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