Asymptotic behavior of the least common multiple of consecutive reducible quadratic progression terms

TL;DR

This paper investigates the asymptotic growth of the least common multiple of consecutive terms in a reducible quadratic progression, establishing a linear growth rate with a specific constant.

Contribution

It provides a new asymptotic formula for the logarithm of the LCM of quadratic progression terms, extending understanding of their number-theoretic behavior.

Findings

Log of LCM grows linearly with n

The growth rate constant depends only on l, m, and f

Asymptotic formula applies to reducible quadratic progressions

Abstract

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $f(x)$ be the product of two linear polynomials with integer coefficients. In this paper, we show that $\log {\rm lcm}_{mn<i\le ln}\{f(i)\}=An+o(n)$, where $A$ is a constant depending only on $l$, $m$ and $f$.