If 6N + 1 and 15N + 2 are divisible by x, then their difference i.e. 9N + 1 will always be divisible by x. Similarly (9N + 1) - (6N + 1) i.e. 3N will also be divisible by x. If x divides 3N then it can also divide 6N. So, x divides 6N and 6N + 1 both i.e. two consecutive numbers. Hence x cannot be anything but 1. So for all the values of N, the given two numbers will be co-prime.