Along the lines of How to map 256 unique strings to 256 unique but effectively arbitrary integers, I am wondering how to generate basically a hashing function. For this question I am wondering if there is a way to perform non-reversible simple operations on integers, such that the resulting output value is always an integer, given two integers as input. So for example, $1 + 2 = 2 + 1$ is reversible. Same with $2 * 3 = 3 * 2$. But while $3 / 2 \neq 2 / 3$, the output values are not integers.
So if there was such an operation, then you could do this:
$3 \circ 2 = 5 \neq 2 \circ 3 = 8$
Something along those lines. Wondering if anything like this exists or where to look for related information. The modulus seems like it might be closely related.