x=9^10–3^17 and x/n is an integer. If n is a positive integer that has exactly two factors, how many different values for n are possible? Select the correct option.
A) 1	B) 2	C) 3	D) 4	E) 5
The expression can be rewritten as (3^2)^10 - 3^17.   Factoring the above we get: 3^17*[(3^3)-1)] = 3^17(26) = 3^17*13*2   The question asks us to find the number of prime factors (number with exactly two factors) of the expression.   From it's factored form we can find that only 2, 3 and 13 will satisfy the above conditions.   Hence Option 3
<result>C</result>
x=9^10–3^17 and x/n is an integer. If n is a positive integer that has exactly two factors, how many different values for n are possible?