what is the remainder when 25! is divided by 29?

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29 is prime. So, 28! mod 29 = 28

25! * 26*27*28 mod 29 = 28

=> R*(-3)*(-2)*(-1) mod 29 = 28
=> -6R mod 29 = 28
or, 23 R mod 29 = 28
When R = 5, the equation becomes 115 mod 29 = 28, which is true.

So, the remainder is 5.