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I have to generate millions of non-repeating random numbers and came across this equation: $x_{i+1} = x_i+c \space(mod \ m)$, where c and m are relative primes and $m \geq total\ to\ be\ generated$.

This works ok since I don't need good random numbers and don't have to memorize them. My question is, what is the demonstration and name of this method? I will have to write about it, but can't find any information not knowing how to formulate my question.

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this is a number generator but not a random number generator – miracle173 Jun 14 '11 at 11:50
If this works for your needs, fine. However, if it is known that you use a linear congruential generator, any math major in the room can easily predict the next "random" number after they have seen a couple. For starters in cracking this, see the recent discussion on this site – Jyrki Lahtonen Jun 14 '11 at 12:01
I added the random tag. Just in case. – Jyrki Lahtonen Jun 14 '11 at 12:24
up vote 5 down vote accepted

Your method is called a "linear congruential generator".

Please have also a look at this question:

how to generate real random numbers

The linear congruential generators are commonly considered to be a bad choice, with much better algorithms available, but it will depend on your application which generator turns out to be good or bad.

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