If one chooses the values of <math>a</math>, <math>c</math> and <math>m</math> with care, then the generator produces a uniform distribution of integers from <math>0</math> to <math>m - 1</math>.
LCG numbers have poor quality. <math>r_n</math> and <math>r_{n + 1}</math> are not independent, as true random numbers would be. Anyone who knows <math>r_n</math> can predict <math>r_{n + 1}</math>, therefore LCG is not cryptographically secure. The LCG is still good enough for simple tasks like [[Miller-Rabin primality test]], or [[deal cards for FreeCell|FreeCell deals]]. Among the benefits of the LCG, one can easily reproduce a sequence of numbers, from the same <math>r_0</math>. One can also reproduce such sequence with a different programming language, because the formula is so simple.
The task is to replicate two historic random number generators. One is the <code>rand()</code> function from [[:Category:BSD libc|BSD libc]], and the other is the <code>rand()</code> function from the Microsoft C Runtime (MSCVRT.DLL). Each replica must yield the same sequence of integers as the original generator, when starting from the same seed.
In these formulas, the seed becomes <math>state_0</math>. The random sequence is <math>rand_1</math>, <math>rand_2</math> and so on.
