# Non-reversible primitive operations on integers [closed]

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.

## closed as unclear what you're asking by Lord Shark the Unknown, mrtaurho, José Carlos Santos, ancientmathematician, metamorphyFeb 6 at 13:53

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• Like subtraction, for instance? – Lord Shark the Unknown Feb 6 at 4:16
• Subtraction is good, but I am wondering for an array of possible types of operations, something with some substance. – Lance Pollard Feb 6 at 4:17