A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(12) + 5; g(12) + 6; g(12) + 7; and g(12) + 8?
Choose the correct choice from the following answers
A) 1	B) 2	C) 3	D) 4	E) none
g(12) is the product of all integers from 1 to 12, so g(12) = 12!   Thus g(12) is a multiple of all the integers from 1 to 12.   Then g(12) is a multiple of 7, 8, 9, and 10.   7 divides g(12)+7   8 divides g(12)+8   9 divides g(12)+9   10 divides g(12)+10   The answer is none.
<result>E</result>
A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(12) + 5; g(12) + 6; g(12) + 7; and g(12) + 8?