Tell Wolfram Alpha that a variable is a natural number

Just add an "assuming x integer" at the end. I tested it, and it seems to work. (similar to Maple's notation assuming x::integer, I guess) For natural it doesn't seem to work properly: assuming x natural

As dirty as this is, I've used modulus 1 to force numbers to be integers. Combine with a >= 0 restriction and you can reach Natural numbers.

Example

It depends on how you are trying what it is you are trying to solve. Telling Mathematica that something is an integer has a different syntax depending on what you are trying to do.

Assuming that you are using the "Solve" function, it would look like this:

Solve[(x - 3/2) (x - 2)== 0 && x \[Element] Integers]

EDIT. After 6 years, the website has changed and this no longer works. However,

 Solve (x-3/2)(x-2)=0 for x integer

seemed to work, as you can can see here.

Solve[ ..., Element[..., Integers]]