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9 years, 2 months ago
find the remainder when 28! is divided by 899?
8 years, 9 months ago
can you send me detailed answer of this question Aaditya sir
9 years, 2 months ago
Using Wilson's theorem,
28! + 1 is divisible by 29 and
30! + 1 is divisible by 31.
30! + 1 = 0 (mod 31)
So 28! *(31-1)*(31-2) + 1 = 0 (mod 31)
So, 28! + 16 = 0 (mod 31)
and 28! + 1 = 0 (mod 29)
So, 28! + 233 = 0 (mod 899).
Hence, remainder is 666