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arXiv · 2411.11316

On the Density of naturals $n$ coprime to $\lfloor P(n) \rfloor$ for certain Classes of Polynomials

Aahan Chatterjee
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Abstract

We obtain asymptotic bounds on the number of natural numbers less than $X$ satisfying $\gcd{\left(n,\lfloor P(n) \rfloor\right)}=1$, under some diophantine conditions on the coefficient of $x$ in $P$, and show that the density of such naturals is exactly $\dfrac{1}{\zeta{\left(2\right)}}$.

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BibTeXRIS

Aahan Chatterjee. 2024-11-18. On the Density of naturals $n$ coprime to $\lfloor P(n) \rfloor$ for certain Classes of Polynomials. https://arxiv.org/abs/2411.11316

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