Thread: Nonnegative integers problem

Let , which is the product of the first six primes. How many nonnegative integers less than have the property that divides ?

I'm not sure how to do this in a more direct way ... here's what I got so far:



So, or

The first case gives us , and nothing else since

The second case has no solutions, and I may be wrong here somewhere (it's late in my part of the world )

, since N is the product of the first 6 primes, this includes 2 ... so . But, will be even, and by adding 1, you get an odd number, so 2 can't divide .

So ... I believe the answer is that there is only 1 solution, which is when