Publications and Preprints

1. On perfect powers that are sums of cubes of a nine term arithmetic progression, with N. Coppola, M. Curcó-Iranzo, M. Khawaja and Ö. Ülkem,

to appear in Indagationes Mathematicae, (arXiv).

2. Power values of power sums: a survey, with N. Coppola, M. Curcó-Iranzo, M. Khawaja and Ö. Ülkem, 

to appear in Women in Numbers Europe 4 - Research Directions in Number Theory, Association for Women in Mathematics Series, Springer, (arXiv).

3. Odd values of the Ramanujan tau function , with M. A. Bennett, A. Gherga and S. Siksek, 

Mathematische Annalen, 382 (2022), no. 1--2, 203--238, (arXiv).

4. A Lucas-Lehmer approach to generalised Lebesgue-Ramanujan-Nagell equations, 

Ramanujan Journal, 56(2) (2021), 585--596, (arXiv).

5. Perfect powers that are sums of squares of an arithmetic progression, with D. Kundu, 

Rocky Mountain Journal of Mathematics, 51(3) (2021), 933--949, (arXiv).

6. On perfect powers that are sums of cubes of a seven term arithmetic progression, with A. Argáez-García, 

Journal of Number Theory, 214 (2020), 440--451, (arXiv | published version).

7. On perfect powers that are sums of cubes of a three term arithmetic progression, with A. Argáez-García, 

Journal of Combinatorics and Number Theory, 10(3) (2019), 147--160, (arXiv | published version).

8. Shifted powers in Lucas-Lehmer sequences, with M. A. Bennett and S. Siksek, 

Research in Number Theory, 5(1) (2019), Art. 15, 27 pp., (arXiv | published version).

9. Perfect powers that are sums of squares in a three term arithmetic progression, with A. Koutsianas, 

International Journal of Number Theory, 14(10) (2018), 2729--2735, (arXiv | published version).

10. Perfect powers that are sums of consecutive squares, 

C. R. Math. Rep. Acad. Sci. Canada, 40(2) (2018), 33--38, (arXiv | published version).

11. On perfect powers that are sums of two Fibonacci numbers, with F. Luca, 

Journal of Number Theory, 189 (2018), 90--96, (arXiv | published version).

12. On the difference between permutation polynomials, with N. Anbar, A. Odžak, L. Quoos, A. Somoza, A. Topuzoğlu, 

Finite Fields and their Applications, 49 (2018), 132--142, (arXiv | published version).

13. On the Carlitz rank of permutation polynomials over finite fields: recent developments, with N. Anbar, A. Odžak, L. Quoos, A. Somoza and A. Topuzoğlu, 

Women in Numbers Europe II  (2018) 39--55, Assoc. Women Math. Ser., 11, Springer, Cham., (published version).

14. On powers that are sums of consecutive like powers, with S. Siksek, 

Research in Number Theory, 3 (2017), Art. 2, 7 pp., (arxiv | published version).

15. Perfect powers that are sums of consecutive cubes, with M. A. Bennett and S. Siksek, 

Mathematika, 63 (2017), no. 1, 230--249, (arXiv | published version).

16. Superelliptic equations arising from sums of consecutive powers, with M. A. Bennett and S. Siksek, 

Acta Arithmetica, 172 (2016), no. 4, 377--393, (arXiv | published version).

Thesis

• Perfect powers that are sums of consecutive like powers. PhD thesis, University of Warwick (2017). 

• Irrationality of some p-Adic Integers. MMath Dissertation, University of Warwick (2012).