If r, q are rationals, and r+q, r*q are integers, are r, q both integers?

Well, the title pretty much says it all. If: , then is it necessarily true that both

I've done some experimenting, and it seems to be true. I mean, 2 and 1/2 satisfy the product, but not the sum, and 1/3, 2/3 satisfy the sum but not the product, but attempts to prove it have so far failed.

I tried saying, let p, q be represented by . Then, , and as such, hcf(ac) and hcf(ad+bc) must be some multiple of hcf(bd), but it didn't get me anywhere. Does anyone have any suggestion as to the next step to go for this?

**On another note, is there a sticky anywhere with advice as to the syntax of the [ MATH ] tag?**