Additive problems with smooth integers
Volume 175 / 2016
Acta Arithmetica 175 (2016), 301-319
MSC: Primary 11P55; Secondary 11N25.
DOI: 10.4064/aa8205-9-2016
Published online: 30 September 2016
Abstract
We study the number $R_s(n)$ of representations of a positive integer $n$ $(\le X)$ in the form $n=m^2+l$ where $m$ is a natural number and $l$ is a $Y$-smooth integer. An analogous problem is also discussed for the number $R_p(n)$ of representations of $n \ (\le X)$ in the form $n = p+l$ where $p$ is a prime number and $l$ is again a $Y$-smooth number.
