# Questions tagged [arithmetic-dynamics]

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### Greatest common divisor of a^{2^n}-1 and b^{2^n}-1

Let a and b be coprime integers. Do we know, expect, or unexpect that there are infinitely many primes p which divide $gcd(a^{2^n} - 1, b^{2^n}-1)$ for some n? Certainly any Fermat prime will ...
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### Rational maps whose complex conjugate equals a PGL conjugate

Let $f(z)\in\mathbb{C}(z)$ be a rational function, and let $\bar{f}(z)$ denote the function obtained by taking the complex conjugate of the coefficients of $f$. I am interested in maps $f$ for which ...
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### If you were to axiomatize the notion of entropy …

What are the axioms that a good notion of entropy must satisfy? Please note that I am not asking for the definitions of various types of entropy such as topological entropy or measure-theoretic ...
Let $p$ be a prime, and consider the sequence $x_0, x_1, \dots$ of elements of the finite field $\mathbf F_p$ given by $x_0 = 0$ and $x_{i+1} = x_i^2 + 1$ for all $i \ge 0$. This sequence must ...