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

Abstract

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We give the answer to the question in the title by proving that L 18 = 5778 = 5555 + 222 + 1 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.

How to cite

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Adegbindin, 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

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