Question

WILSON THEOREM STATES THAT IF 'N' IS A PRIME NUMBER , THAT N DIVIDES (N-1)! +1 . USING THIS FIND THE SMALLEST DIVISOR OF 12!+6!+12! * 6! + 1

Answer 1

12!+6!+12!*6!+1
=(12!+1)+6!(1+12!)
=(1+12!)(1+6!)
since N divides (N-1)!+1, this means(12!+1)divisible by(12+1)i.e 13
AND (6!+1) divisible by(6+1) i.e 7
therefore divisor 13*7=91

Answer 2

The answer is 7.

12! + 6! +12!x6! +1, can be written as

12! + 6!*12! + 6!+1

= 12!(6! +1) + 6!+1

= (12!+1)(6!+1)

So this number is divisible by 13 and 7. The smaller of the two is 7 so 7 must be the answer