Question

The number of positive n in the range 12=<n=<40 such that the product (n-1)(n-2)........3.2.1 is not divisible by n is

Answer 1

The answer should include 29 also Wilson's theorem says that (n-1)! plus 1 is always divisible by n ONLY when n is prime. That means, n will not divide (n-1)! and give 1 as the remainder if n is prime.

Answer 2

Answer:positive integers n is in the range 12<n<40 such that the product (n-1)*(n-2)*.....3*2 is not divisible by n, implies that n should be a prime no . so there are 7 prime nos in the given range.

therefore, option (B).

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