Qian-Rong Tan

collaborators

3 papers

math.NT2012

New Lower Bounds for the Least Common Multiples of Arithmetic Progressions

Rongjun Wu, Qianrong Tan, Shaofang Hong

For relatively prime positive integers $u_{0}$ and $r$ and for $0 \leq k \leq n$ , define $u_{k} := u_{0} + k r$ . Let $L_{n} := lcm (u_{0}, u_{1}, ..., u_{n})$ and let $a, l \geq 2$ be any integers. In t…

math.NT2012

On the periodicity of a class of arithmetic functions associated with multiplicative functions

Guoyou Qian, Qianrong Tan, Shaofang Hong

Let $k \geq 1, a \geq 1, b \geq 0$ and $c \geq 1$ be integers. Let $f$ be a multiplicative function with $f (n) \neq = 0$ for all positive integers $n$ . We define the arithmetic function $g_{k,f…

math.NT2011

The least common multiple of a sequence of products of linear polynomials

Shaofang Hong, Guoyou Qian, Qianrong Tan

Let $f (x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $lo g lcm (f (1), ..., f (n)) \sim A n$ as $n\rightarrow\…