1956 AHSME Problems/Problem 48
If is a positive integer, then can be a positive integer, if and only if is:
Lets begin by noticing that:
Therefore, in order for to be a positive integer, must be a non-negative integer. Since the bottom the the fraction is an odd number, we can multiply the top of by 2 without changing whether it is an integer or not. Therefore, in order for to be an integer, must also be an integer. As a result, must be a factor of 65, or . Therefore must be at least 3, and less than or equal to 35. So the answer which best fits these constraints is .