### Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

**Austrian Science Fund (FWF): W1230 **

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

### Project 13:

Additive and combinatorial number theory

#### Publications 2018

[16] | On Romanov's constant, Mathematische Zeitschrift, (2018). (to appear)
[bib] [doi/article] | ,

[15] | The number of solutions of the Erd\H os-Straus equation and sums of $k$ unit fractions, (2018). (submitted)
[bib] [arXiv] | ,

[14] | Romanov type problems, The Ramanujan Journal, (2018). (to appear)
[bib] [doi/article] | ,

#### Publications 2017

[13] | Prescribing the binary digits of squarefree numbers and quadratic residues, Trans. Amer. Math. Soc., 369, 8369-8388, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

[12] | Number theory---Diophantine problems, uniform distribution and applications, (Christian Elsholtz, Peter Grabner, eds.), Springer, xv+444, (2017). (Festschrift in honour of Robert F. Tichy's 60th birthday)
[bib] [MR] [doi/article] |

[11] | On the regularity of primes in arithmetic progressions, Int. J. Number Theory, 13(5), 1349—1361, (2017).
[bib] [MR] [doi/article] | ,

[10] | On Erd\H os and Sárközy's sequences with Property P, Monatsh. Math., 182(3), 565—575, (2017).
[bib] [MR] [doi/article] | ,

#### Publications 2015

[9] | Romanov's Theorem in Number Fields, (2015). (preprint)
[bib] [arXiv] | ,

[8] | Additive decompositions of sets with restricted prime factors, Trans. Amer. Math. Soc., 367(10), 7403—7427, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[7] | Hilbert cubes in arithmetic sets, Rev. Mat. Iberoam., 31(4), 1477—1498, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[6] | On conjectures of T. Ordowski and Z. W. Sun concerning primes and quadratic forms, Chapter in Analytic number theory (C. Pomerance, M. Rassias, eds.), Springer, 65—81, (2015).
[bib] [MR] [doi/article] | ,

#### Publications 2014

[5] | On Diophantine quintuples and $D(-1)$-quadruples, Monatshefte für Mathematik, 175, 227-239, (2014).
[bib] [MR] [doi/article] | ,

#### Publications 2013

[4] | Sumsets being squares, Acta Mathematica Hungarica, 141(4), 353-357, (2013).
[bib] [MR] [doi/article] | ,

[3] | On gaps between primitive roots in the Hamming metric., Quarterly Journal of Mathematics, 64(4), 1043—1055, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[2] | The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Transactions on Information Theory, 59, 1065-1075, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2012

[1] | Hilbert cubes in progression-free sets and in the set of squares, Israel Journal of Mathematics, 192(1), 59-66, (2012).
[bib] [MR] [doi/article] | ,