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Which of the following is a divisor of 12! · 6! + 12! + 6! + 1?

A. 21
B. 77
C. 91
D. 115
E. 143

Hint : Use Wilson's Theorem[tex].[/tex]​

Respuesta :

mhanifa

Answer:

  • C. 91

Step-by-step explanation:

Rewriting the given as factors:

  • 12! · 6! + 12! + 6! + 1 =
  • 12!(6! + 1) + (6! + 1) =
  • (12! + 1)(6! + 1) =
  • ((13 - 1)! + 1)((7 - 1)! + 1)

As per Wilson's theorem, if n is prime number, (n - 1)! + 1 is divisible by n

As per above, 13 and 7 are both prime numbers, so the expression is divisible by both 7 and 13:

  • 7*13 = 91

So correct choice is C