Research

Research interests:

I am a mathematician whose research interests lie at the interface between pure and applied mathematics. I am currently interested in number theory, more specifically working on topics from Diophantine equations which involve linearly recurrent sequences such as the Fibonacci numbers, Pell numbers, Lucas numbers, Tribonacci numbers, Padovan numbers and the k-generalized Fibonacci numbers. The methods of approach to such equations heavily rely on the Baker's theory for linear forms in logarithms of algebraic numbers as well as the Baker-Davenport reduction procedure.

My papers on Google Scholar, HAL, arXiv, COE, MathSciNet, zbMATH, ORCID; My Edős Number is 2. Thanks to Florian Luca. Here are my PhD ancestors MGP. 

Publications:

• Herbert Batte, Mahadi Ddamulira,  Juma Kasozi and Florian Luca. Multiplicative independence in the sequence of  k-generalized Lucas numbers.Indag. Math.  (2024),  19pp. HAL, arXiv, MR, Zb, DOI, DOI-COE. [ScienceDirect]

• Herbert Batte, Mahadi Ddamulira,  Juma Kasozi and Florian Luca. On the exponential diophantine equation U_n^x + U_n+1^x = U_m. Ramanujan J. 64 (2024), No. 1, 153--184. HAL, arXiv, MR474026, Zbl07845631, DOI, DOI-COE. [SharedIt]

• Mahadi Ddamulira and Florian Luca. On the x-coordinates of Pell equations which are products of two Pell numbers. Math. Slovaca  74 (2024), No. 1, 41--56. HAL, arXiv, MR4745442, Zbl7859869, DOI, DOI-COE. 

• Mahadi Ddamulira, Paul Emong, and Geoffrey Ismail Mirumbe. Palindromic concatenations of two distinct repdigits in Narayana's cows sequence. Bull. Iranian Math. Soc. 50 (2024), No. 3, Art. No. 35, 16pp. HAL, arXiv, MR4735871, Zbl, DOI, DOI-COE. [SharedIt]

• Herbert Batte, Mahadi Ddamulira, Juma Kasozi, and Florian Luca. On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime . Glasnik Mat. 57 (2022), No.2, pp 185--200. HAL, arXiv, MR4541293, Zbl07644252, DOI, DOI-COE. [Open Access (HRČAK)]

• Herbert Batte, Taboka P Chalebgwa, and Mahadi Ddamulira. Perrin numbers that are concatenations of two repdigits.  Arab. J. Math. 11 (2022), No.3, pp 469--478. HAL, arXiv, MR4502865, Zbl07610698, DOI, DOI-COE. [SharedIt]

• Mahadi Ddamulira, Florian Luca, and Robert Tichy. On the  Shorey-Tijdeman Diophantine equation involving terms of Lucas sequences. Indag. Math. (N.S.) 33 (2022), No. 2, pp 314--321. HAL, arXiv, MR4383112, Zbl07478442, DOI, DOI-COE.  [Open Access]

• Mahadi Ddamulira and Florian Luca. On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. Ramanujan J. 56 (2021), No. 2, pp 651--684. HAL, arXiv, MR4325998, Zbl07434820, DOI, DOI-COE. [SharedIt]

• Taboka P Chalebgwa and Mahadi Ddamulira. Padovan numbers which are palindromic concatenations of two distinct repdigits. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), No.3, Art. No. 108, 14 pp.  HAL, arXiv, MR4249964, Zbl07358923, DOI, DOI-COE. [SharedIt]

• Mahadi Ddamulira. Padovan numbers that are concatenations of two distinct repdigits. Math. Slovaca 71 (2021), No. 2, pp 275 --284. HAL, arXiv, MR4243626, Zbl07438341, DOI, DOI-COE. [Access]

• Mahadi Ddamulira. On the x-coordinates of Pell equations that are sums of two Padovan numbers. Bol. Soc. Mat. Mex. (3) 27 (2021), No. 1, Art. No. 4, 23 pp. HAL, arXiv, MR4219361, Zbl07342824, DOI, DOI-COE. [SharedIt]

• Mahadi Ddamulira and Florian Luca. The x-coordinates of Pell equations and sums of two Fibonacci numbers II.  Proc. Indian Acad. Sci. (Math. Sci.) 130 (2020), No.1, Art. No. 58, 21 pp.  HAL, arXiv, MR4156322, Zbl07271355, DOI, DOI-COE. [SharedIt]

• Mahadi Ddamulira. Tribonacci numbers that are concatenations of two repdigits. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), No.4, Art. No. 203, 10 pp. HAL, arXiv, MR4151771, Zbl07262208, DOI, DOI-COE. [SharedIt]

• Mahadi Ddamulira. On the x-coordinates of Pell equations that are products of two Padovan numbers. Integers 20 (2020), Art. No. A70, 20 pp. HAL, arXiv, MR4142507, Zbl, DOI-COE. [Open Access]

• Mahadi Ddamulira and Florian Luca. On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3. Int. J. Number Theory 16 (2020), No.7, pp 1643--1666. HAL, arXiv, MR4132045, Zbl07232845, DOI. [Open Access]

• Mahadi Ddamulira. Repdigits as sums of three balancing numbers. Math. Slovaca 70 (2020), No.3, pp 557--566. HAL, arXiv, MR4104345, Zbl07289661, DOI, DOI-COE. [Access]

• Mahadi Ddamulira. Diophantine Equations and Linearly Recurrent Sequences. Thesis (Dr.rer.nat.) - Technische Universtaet Graz (Austria). (2020), 183 pp. ISBN:  979-8662-39876-4, MR4132436, ProQuest LLC. [Open Access] (Defended 05.06.2020, Slides DOI-COE).

• Mahadi Ddamulira. On the x-coordinates of Pell equations that are products of two Lucas numbers. Fibonacci Quart. 58 (2020), No.1, pp 18--37. HAL, arXiv, MR4069678, Zbl07240183, DOI-COE Link. [Access]

• Mahadi Ddamulira and Florian Luca. On the x-coordinates of Pell equations which are k-generalized Fibonacci numbers. J. Number Theory 207 (2020), pp 156--195. HAL, arXiv, MR4017944, Zbl07118782, DOI. [Open Access]

• Mahadi Ddamulira. Repdigits as sums of three Padovan numbers. Bol. Soc. Mat. Mex. (3)  26 (2020), No. 2, pp 247--261. HAL, arXiv, MR4110448, Zbl07211802, DOI. [SharedIt]

• Mahadi Ddamulira. On the problem of Pillai with Fibonacci numbers and powers of 3. Bol. Soc. Mat. Mex. (3) 26 (2020), No. 2, pp 263--277. HAL, arXiv, MR4110449, Zbl07211803, DOI. [SharedIt]

• Mahadi Ddamulira. On the problem of Pillai with Padovan numbers and powers of 3. Stud. Sci. Math. Hungar. 56 (2019), No.3, pp 364--379. HAL, arXiv, MR4020341, Zbl1438.11034 DOI. [Access]

• Mahadi Ddamulira. On the problem of Pillai with Tribonacci numbers and powers of 3. J. Integer Seq. 22 (2019), No. 5, Article 19.5.6, 14 pp. HAL, arXiv, MR4008154, Zbl07114878, Link. [Open Access]

• Mahadi Ddamulira, Carlos Alexis Gómez-Ruiz, and Florian Luca. On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2. Monatsh. Math. 187 (2018), No. 4, pp 635--664. arXiv, MR3861322, Zbl1437.11051, DOI. [SharedIt] 

• Mahadi Ddamulira, Florian Luca, and Mihaja Rakotomalala. On a problem of Pillai with Fibonacci numbers and powers of 2. Proc. Indian Acad. Sci. Math. Sci. 127 (2017), No. 3, pp 411--421. arXiv, MR3660342, Zbl1421.11017, DOI. [SharedIt]

• Mahadi Ddamulira. The Algorithmic Solution of Diophantine Equations. LAP LAMBERT Academic Publishing (2016), ISBN 978-3-330-00696-6.

• Mahadi Ddamulira, Florian Luca, and Mihaja Rakotomalala. Fibonacci numbers which are products of two Pell numbers. Fibonacci Quart. 54 (2016), No. 1, pp 11--18. arXiv, MR3473255, Zbl1400.11040, Link.

Accepted papers:

Preprints:

Citations (from other mathematicians):

• J. J. Bravo,  F. Luca, and K. Yazán. On Pillai's problem with Tribonacci numbers and powers of 2. Bull. Korean Math. Soc. 54 (2017), No. 3, pp 1069--1080. MR3659165 Zbl1379.11013

• K. C. Chim, I. Pink,  and V.  Ziegler. On a variant of Pillai's problem. Int. J. Number Theory 13 (2017), No. 7, pp 1711--1727.  MR3667491 Zbl06756824

• S. Pinelas,  G. B. A. Xavier,  S. U. Vasantha Kumar,  and M. Meganathan. Laplace-Fibonacci transform by the solution of second order generalized difference equation. Nonauton. Dyn. Syst. 4 (2017), No. 1, pp 22--30. MR3694371 Zbl1377.39033

• K. C. Chim, I. Pink,  and V. Ziegler. On a variant of Pillai's problem II. J. Number Theory 183 (2018), pp 269--290. MR3715237 Zbl06802534

• C. Bertók and L. Hajdu.  A Hasse-type principle for exponential Diophantine equations over number fields and its applications. Monatsh. Math. 187 (2018), No. 3, pp 425--436. MR3858424 Zbl06955341

• Z. Şiar. Lucas numbers which are products of two balancing numbers. Notes from the International Autumn School on Computational Number Theory, pp 355--363, Tutor. Sch. Workshops Math. Sci., Birkhäuser/Springer, Cham, 2019. MR3932025 Zbl

• K. C. Chim and V. Ziegler. On Diophantine equations involving sums of Fibonacci numbers and powers of 2. Integers 18 (2018), Paper No. A99, 30 pp. MR3893666 Zbl1416.11047

• A.C. García Lomelí, S. Hernández Hernández, and F. Luca. Pillai's problem with the Padovan and tribonacci sequences. Indian J. Math. 61 (2019), No. 1,  pp 61--75. MR3931607 Zbl07116888

• M. O. Hernane, F. Luca, S. E. Rihane, and A. Togbé.  On Pillai's problem with Pell numbers and powers of 2. Hardy-Ramanujan J. 41 (2018), pp 22--31. MR3935493 Zbl07101941

• Z. Şiar, F. Erduvan, and R. Keskin. Repdigits as product of two Pell or Pell-Lucas numbers. Acta Math. Univ. Comenian. (N.S.) 88 (2019), No. 2, pp 247--256. MR3984643 Zbl07111088

• A. C. García Lomelí and S. Hernández Hernández. Pillai's problem with Padovan numbers and powers of two. Rev. Colombiana Mat. 53 (2019), No. 1, pp 1--14. MR3996173 Zbl07114211

• F. Erduvan and  R. Keskin. Fibonacci and Lucas numbers as products of two repdigits. Turkish J. Math. 43 (2019), No. 5, 2142--2153. MR4020376 Zbl07164294

• S. Hernández Hernández, F. Luca, and L. M.  Rivera. On Pillai's problem with the Fibonacci and Pell sequences. Bol. Soc. Mat. Mex. (3) 25 (2019), No. 3, pp 495--507. MR4022301 Zbl07137966

• F. Erduvan and R. Keskin. Repdigits as products of two Fibonacci or Lucas numbers. Proc. Indian Acad. Sci. Math. Sci. 130 (2020), No. 1, Paper No. 28. MR4079185 Zbl07184523

• F. Erduvan and R. Keskin. Fibonacci numbers which are products of two balancing numbers. Ann. Math. Inform. 50 (2019), pp 57--70. MR4048804  Zbl07174839

• A. C. García Lomelí, S. Hernández Hernández, and F. Luca. Pillai’s problem with the Fibonacci and Padovan sequences. Ann. Math. Inform. 50 (2019), pp 101--115. MR4048808 Zbl07174843

• H. Erazo, C. A. Gómez-Ruiz, and F. Luca. Linear combinations of prime powers in X-coordinates of Pell equations. Ramanujan J. 53 (2020), No. 1, pp 123--137. MR4148461 Zbl07343717

• P. Trojovský. Fibonacci numbers with a prescribed block of digits. Mathematics 8 (2020), No. 4, pp 1--7,  Art. 639. MR Zbl

• P. Trojovský. On the Characteristic Polynomial of the Generalized k-Distance Tribonacci Sequences. Mathematics 8 (2020), No. 8, pp 1--8,  Art. 1387. MR Zbl

• S. E. Rihane, Y. Akrour, and A. El Habibi. Fibonacci numbers which are products of three Pell numbers and Pell numbers which are products of three Fibonacci numbers. Bol. Soc. Mat. Mex. (3) 26 (2020), No. 3, pp 895--910. MR4155336 Zbl07270781

• L. Hajdu and P. Sebestyén. Sums of S-units in the solution sets of generalized Pell equations. Arch. Math. (2020), pp 279--287. MR4134922  Zbl07238497

• A. Alahmadi, A. Altassan, F. Luca, and H. Shoaib. Products of k-Fibonacci numbers which are rep-digits. Publ. Math. Debrecen. 97 (2020), No. 1-2, pp 101--115. MR4128145 Zbl07287377

• K. Liptai, L. Németh, G. Soydan,  and L. Szalay. Resolution of the equation (3^{x_1}-1)(3^{x_2}-1)=(5^{y_1}-1)(5^{y_2}-1).  Rocky Mountain J. Math. 50 (2020), No. 4, pp 1425--1433. MR4154815 Zbl07261872

• F. Luca and L. Szalay.  On the equation (2k −1)(3ℓ −1) = 5m −1. Azerbaijan J. Math. 10 (2020), No. 2, pp 3--11. MR4154123 Zbl07293028

• A. Alahmadi, A. Altassan, F. Luca, and H. Shoaib. k-generalized Fibonacci numbers which are concatenations of two repdigits. Glas. Mat. Ser. III.  (2020), No., pp 1--18. MR Zbl

• D. Bednařík and E. Trojovská. Repdigits as Product of Fibonacci and Tribonacci Numbers . Mathematics 8 (2020), No. 10, pp 1--8,  Art. 1720. MR Zbl

• P. Trojovský. On Repdigits as Sums of Fibonacci and Tribonacci Numbers . Symmetry 12 (2020), No. 11, pp 1--7,  Art. 1774. MR Zbl

• A. Dubickas. Pillai’s Equation in Polynomials. Mediterr. J. Math. 18 (2021), No. 2, pp 1--10,  Paper No. 63. MR4218375 Zbl07321620

• R. Tichy, I. Vukusic, D.Yang, and V. Ziegler. Integers representable as differences of linear recurrence sequences. Res. Number Theory. 7 (2021), No. 2, pp 1--12,  Paper No. 24. MR4232907 Zbl07336790

• C. Fuchs and S. Heintze. A function field variant of Pillai's problem. J. Number Theory. 222 (2021), pp 278--292. MR4215817 Zbl07318739

• H. S. Erazo and C. A. Gómez. An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and x-coordinates of Pell equations. Period. Math. Hungar. 83 (2021), No.2,  pp 165--184. MR4344125 Zbl07434713

• F. Erduvan and R. Keskin. Lucas numbers which are concatenations of two repdigits. Bol. Soc. Mat. Mex. (3) 27 (2021), No. 1, Paper No. 20. MR4220811 Zbl07342803