Finding Remainder!
Number Theory
Level
2
Find the remainder when (12!+13!+14!+15!+16!+.............221119992000066698732798999975!) is divided by 13.
Details and Assumptions.
Remainder is always positive.
The answer is 12.
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1 solution
13!,14!....n! where n>13 is always divisible by 13.Hence,remainder(R)=0.Now,we know that(p-1)! is congurent to -1(mod p).Now,13 is prime.So,12! is congurent to -1(mod 13).So,the R=12