Uniform lower bound for the least common multiple of a polynomial sequence

Shaofang Hong, Yuanyuan Luo, Guoyou Qian +1

Let $n$ be a positive integer and $f(x)$ be a polynomial with nonnegative integer coefficients. We prove that ${\mathrm{lcm}}_{\lceil n/2\rceil \le i\le n}\{f(i)\}\ge 2^n$ except that…