Fibonacci or Lucas Numbers Which are Products of Two Repdigits in Base b
In this study, we find all Fibonacci and Lucas numbers which can be expressible as a product of two repdigits in the base b . It is shown that the largest Fibonacci and Lucas numbers which can be expressible as a product of two repdigits are F 12 = 144 and L 15 = 1364 , respectively. Also, we have t...
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| Veröffentlicht in: | Boletim da Sociedade Brasileira de Matemática 2021-12, Vol.52 (4), p.1025-1040 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this study, we find all Fibonacci and Lucas numbers which can be expressible as a product of two repdigits in the base
b
. It is shown that the largest Fibonacci and Lucas numbers which can be expressible as a product of two repdigits are
F
12
=
144
and
L
15
=
1364
, respectively. Also, we have the presentation
F
12
=
144
=
6
×
(
3
+
3
·
7
)
=
(
6
)
7
×
(
33
)
7
=
4
×
(
4
+
4
·
8
)
=
(
4
)
8
×
(
44
)
8
and
L
15
=
1364
×
(
22222
)
4
=
2
×
(
2
+
2
·
4
+
2
·
4
2
+
2
·
4
3
+
2
·
4
4
)
. |
|---|---|
| ISSN: | 1678-7544 1678-7714 |
| DOI: | 10.1007/s00574-021-00243-y |