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Happy New Year, MO community! We need someone expert in Generalized Continued Fractions (GCFs), with a deep knowledge of the GCFs’ convergence properties, to solve the following problem. PROBLEM ...

Let $p_1,\dotsc,p_k: \mathbb{N} \to \mathbb{Z}$ be rationally independent polynomials with zero constant term. If $t_1,\dotsc,t_k \in [0,1)$ are not all rational, is it true that the polynomial $$p(n)...

An rr function (i.e. rational rational function) is a quotient $$ \frac fg\,:\, \Bbb Q\ \to\ \Bbb Q\cup\{\infty\} $$ such that $\ f,g\,\in\,\Bbb Z[X],\ $ where $\ g\ne 0.$ QUESTION Do there exist ...