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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Expected period of quadratic generator

I am interested in the mean period of a quadratic congruential generator. Let $X_{n+1} = \sum_{i=0}^2 a_i X_n^i \bmod m$ where the $a_i \in \mathbb{Z_m}$ are chosen uniformly at random and $m$ is a fi …
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