Given a number, produce another random number that is the same every time and distinct from all other results

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This sounds like a non-repeating random number generator. There are several possible approaches to this.

As described in this article, we can generate them by selecting a prime number p and satisfies p % 4 = 3 that is large enough (greater than the maximum value in the output range) and generate them this way:

int randomNumberUnique(int range_len , int p , int x)
    if(x * 2 < p)
       return (x * x) % p
    else
       return p - (x * x) % p

This algorithm will cover all values in [0 , p) for an input in range [0 , p).

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