Question

What is the remainder when 38 factorial is divided by 41?
no copy or spam or improper answer or excuse is allowed. well explanation is needed.!!

Answer 1

By Wilson's theorem,

(n-2)! mod n = 1 if n is prime

39! Mod 41 = 1

39*38*x mod 41 = 1

(-2)*(-3)x mod 41 = 1

6x mod 41 =1

6x mod 41= 41n+1

Keep n = 1

x mod 41 =42/6

X mod 41 = 7

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