Can a Lucas number be a sum of three repdigits?
Chèfiath A. Adegbindin; Alain Togbé
Commentationes Mathematicae Universitatis Carolinae (2020)
- Volume: 61, Issue: 3, page 383-396
- ISSN: 0010-2628
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topAdegbindin, Chèfiath A., and Togbé, Alain. "Can a Lucas number be a sum of three repdigits?." Commentationes Mathematicae Universitatis Carolinae 61.3 (2020): 383-396. <http://eudml.org/doc/297364>.
@article{Adegbindin2020,
abstract = {We give the answer to the question in the title by proving that \begin\{equation*\} L\_\{18\} = 5778 = 5555 + 222 + 1 \end\{equation*\}
is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.},
author = {Adegbindin, Chèfiath A., Togbé, Alain},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Pell equation; repdigit; linear forms in complex logarithms},
language = {eng},
number = {3},
pages = {383-396},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Can a Lucas number be a sum of three repdigits?},
url = {http://eudml.org/doc/297364},
volume = {61},
year = {2020},
}
TY - JOUR
AU - Adegbindin, Chèfiath A.
AU - Togbé, Alain
TI - Can a Lucas number be a sum of three repdigits?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 3
SP - 383
EP - 396
AB - We give the answer to the question in the title by proving that \begin{equation*} L_{18} = 5778 = 5555 + 222 + 1 \end{equation*}
is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.
LA - eng
KW - Pell equation; repdigit; linear forms in complex logarithms
UR - http://eudml.org/doc/297364
ER -
References
top- Adegbindin C., Luca F., Togbé A., Pell and Pell–Lucas numbers as sums of three repdigits, accepted in Acta Math. Univ. Comenian. (N.S.). MR4061423
- Bravo J. J., Luca F., 10.5486/PMD.2013.5390, Publ. Math. Debrecen 82 (2013), no. 3–4, 623–639. MR3066434DOI10.5486/PMD.2013.5390
- Bugeaud Y., Mignotte M., 10.1112/S0025579300007865, Mathematika 46 (1999), no. 2, 411–417. MR1832631DOI10.1112/S0025579300007865
- Bugeaud Y., Mignotte M., Siksek S., 10.4007/annals.2006.163.969, Ann. of Math. (2) 163 (2006), no. 3, 969–1018. MR2215137DOI10.4007/annals.2006.163.969
- Díaz-Alvarado S., Luca F., Fibonacci numbers which are sums of two repdigits, Proc. XIVth International Conf. on Fibonacci Numbers and Their Applications, Morelia, Mexico, 2010, Sociedad Matematica Mexicana, Aportaciones Matemáticas, Investigación, 20, 2011, pages 97–108. MR3243271
- Dossavi-Yovo A., Luca F., Togbé A., 10.5486/PMD.2016.7378, Publ. Math. Debrecen 88 (2016), no. 3–4, 381–399. MR3491748DOI10.5486/PMD.2016.7378
- Faye B., Luca F., Pell and Pell–Lucas numbers with only one distinct digit, Ann. Math. Inform. 45 (2015), 55–60. MR3438812
- Luca F., 10.2989/16073600009485986, Quaest. Math. 23 (2000), no. 4, 389–404. MR1810289DOI10.2989/16073600009485986
- Luca F., Fibonacci and Lucas numbers with only one distinct digit, Portugal. Math. 57 (2000), no. 2, 243–254. MR1759818
- Luca F., Repdigits as sums of three Fibonacci numbers, Math. Commun. 17 (2012), no. 1, 1–11. MR2946127
- Marques D., Togbé A., 10.4064/cm124-2-1, Colloq. Math. 124 (2011), no. 2, 145–155. MR2842943DOI10.4064/cm124-2-1
- Marques D., Togbé A., On repdigits as product of consecutive Fibonacci numbers, Rend. Istit. Mat. Univ. Trieste 44 (2012), 393–397. MR3019569
- Matveev E. M., An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000), no. 6, 125–180 (Russian); translation in Izv. Math. 64 (2000), no. 6, 1217–1269. MR1817252
- de Weger B. M. M., Algorithms for Diophantine Equations, CWI Tract, 65, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1989. MR1026936
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