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9Â years, 1Â month ago
find the remainder when 28! is divided by 899?
8Â years, 8Â months ago
can you send me detailed answer of this question Aaditya sir
9Â years, 1Â month 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
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