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1. On generalized square-full numbers in an arithmetic progression

   Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan in Czechoslovak Mathematical Journal

   Article 14 October 2021

2. Kloosterman Sums and a Problem of D. H. Lehmer

   A classical problem of D. H. Lehmer suggests the study of distributions of elements of Z / p Z of opposite parity to the multiplicative inverse mod p ....

   ** **, Yuan Yi in Chinese Annals of Mathematics, Series B

   Article 14 May 2020

3. Character sums over squarefree and squarefull numbers

   We give upper bounds for character sums over squarefree and squarefull numbers sharper than the prior known in the literature. As an application, we...

   Marc Munsch in Archiv der Mathematik

   Article 26 June 2014

4. On the difference between an integer and its m-th power mod n

   ZheFeng Xu in Science China Mathematics

   Article 11 May 2013

5. Modular hyperbolas

   We give a survey of a variety of recent results about the distribution and some geometric properties of points ( x , y ) on modular hyperbolas ...

   Igor E. Shparlinski in Japanese Journal of Mathematics

   Article 17 November 2012

6. Are quadratic residues random?

   V. I. Arnol’d in Regular and Chaotic Dynamics

   Article 06 August 2010

7. Twins of k-free numbers in arithmetic progressions

   We give a new upper bound of Barban–Davenport–Halberstam type for twins of k -free numbers in arithmetic progressions.

   Zaizhao Meng in Acta Mathematica Hungarica

   Article 03 November 2010

8. An almost all result on \({q_1q_2\equiv c ({\rm mod}\, q)}\)

   Tsz Ho Chan in Monatshefte für Mathematik

   Article 17 September 2009

9. Partitions into two Lehmer numbers

   We prove an asymptotic formula for the number of representations of an integer as sum of two Lehmer numbers which implies that under some natural...

   Igor E. Shparlinski, Arne Winterhof in Monatshefte für Mathematik

   Article 09 June 2009

10. Arithmetics of the numbers of orbits of the Fermat–Euler dynamical systems

    Ricardo Uribe-Vargas in Functional Analysis and Other Mathematics

    Article 01 July 2006

11. On a Problem of D. H. Lehmer

    The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L–functions to study the...

    Hua Ning Liu, Wen Peng Zhang in Acta Mathematica Sinica

    Article 18 June 2005

12. Arithmetic Progressions, Prime Numbers, and Squarefree Integers

    In this paper we establish the distribution of prime numbers in a given arithmetic progression p ≡ l for which ap + b is squarefree.

    Stuart Clary, Jacek Fabrykowski in Czechoslovak Mathematical Journal

    Article 01 December 2004

13. On a Problem of D. H. Lehmer and General Kloosterman Sums

    Let q ≥ 3 be an odd number, a be any fixed positive integer with ( a, q ) = 1. For each integer b with 1 ≤ b < q and ( b, q ) = 1, it is clear that there...

    Wen Peng Zhang in Acta Mathematica Sinica

    Article 01 June 2004

14. Value distribution of g-additive functions

    Necessary and sufficient conditions are given that answer the following questions: When does an integer valued (real valued) g -additive function have...

    Manfred Peter, Jürgen Spilker in manuscripta mathematica

    Article 01 August 2001

15. A Binary Additive Problem of Erdös and the Order of 2 mod p²

    We show that the problem of representing every odd positive integer as the sum of a squarefree number and a power of 2, is strongly related to the...

    Andrew Granville, K. Soundararajan in The Ramanujan Journal

    Article 01 March 1998

16. A Binary Additive Problem of Erdős and the Order of 2 mod p 2

    We show that the problem of representing every odd positive integer as the sum of a squarefree number and a power of 2, is strongly related to the...

    Andrew Granville, K. Soundararajan in Analytic and Elementary Number Theory

    Chapter 1998