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Let $n \in \mathbb{N}$ be a positive integer. It is possible to prove that the equation $F_1(n)=m$ where $m \in \mathbb{Z}$ and $$ F_1(n)=(1+2+\ldots+n)\cdot\left(\frac{1}{1}+\frac{1}{2}+\dots+\frac{1}...

Hilbert 10th problem, while undecidable in general, remains open for 2-variable equations: we do not know if there is an algorithm that, for polynomial $P(x,y)$ with integer coefficients, decides ...