It tells us that
The key there is that u is less than N squared, not just N. Hope that helps. I'm not too familiar with cryptology and stuff, but just from considering that set, , and q would be integers that satisfy the condition, i.e. . There would b N u's also ...
Hope that helps, again, I'm not too familiar with cryptology, so I don't know if there would be any exceptions, or any modifications to how the mod is applied, but just from a basic number theory perspective, and considering that set ... that's what I get. Also, basically
Hope that helps a bit