Abstract
AbstractLet $$ \{P_{n}\}_{n\ge 0} $${Pn}n≥0 be the sequence of Padovan numbers defined by $$ P_0=0 $$P0=0, $$ P_1 =1=P_2$$P1=1=P2, and $$ P_{n+3}= P_{n+1} +P_n$$Pn+3=Pn+1+Pn for all $$ n\ge 0 $$n≥0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.
Publisher
Springer Science and Business Media LLC
Reference12 articles.
1. Bombieri, E., Gubler, W.: Heights in Diophantine Geometry. Cambridge University Press, Cambridge (2006)
2. Bugeaud, Y., Mignotte, M., Siksek, S.: Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers. Ann. Math. 163(2), 969–1018 (2006)
3. Ddamulira, M.: Repdigits as sums of three balancing numbers (preprint) (2019)
4. Dujella, A., Pethő, A.: A generalization of a theorem of Baker and Davenport. Q. J. Math. 49(195), 291–306 (1998)
5. Gúzman Sánchez, S., Luca, F.: Linear combinations of factorials and $$s$$-units in a binary recurrence sequence. Ann. Math. du Qué. 38(2), 169–188 (2014)
Cited by
19 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献