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I want to create a random number function but I don’t want to use any already-made rand() function or method.
Is there a well-known algorithm or theory about it that I would call in?
You almost certainly want a
linear congruential pseudo-random number generator:http://en.wikipedia.org/wiki/Linear_congruential_generator
There are a few criteria in the Wikipedia article to determine whether a given set of parameters will have the maximum period possible.