How to determine the nearest points on the plane by hashing?

Question

Algorithms

I keep reading articles on Wikipedia and Habré, and I will not fully help you understand the essence of hashing methods.
I found such expressions ((x * 73856093 + y * 19349669 + z * 83492791))% n( and the like), but no matter how I try to check them, it doesn’t work out. Although I don’t even understand what should come out, and how I can work with this hash.
I know the hash sets, I project something and in some way inconsistencies crawl out in my view.
For example, in a hash set, the hash is not important to me and the object is located somewhere in this array, the function itself will find it and be done with it.

Answer 1

In fact, in the above article, a slightly different formula is given.
Don't you find that the "^" operation is somewhat different from operations "+"?