Repdigits base b as products of two Fibonacci numbers
Let ( F n ) be the sequence of Fibonacci numbers defined by F 0 = 0 , F 1 = 1 , and F n = F n - 1 + F n - 2 for n ≥ 2 . Let 2 ≤ m ≤ n and b = 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . In this study, we show that if F m F n is a repdigit in base b and has at least two digits, then F m F n ∈ 3 , 4 , 5 , 6 , 8 ,...
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| Veröffentlicht in: | Indian journal of pure and applied mathematics 2021-09, Vol.52 (3), p.861-868 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
(
F
n
)
be the sequence of Fibonacci numbers defined by
F
0
=
0
,
F
1
=
1
, and
F
n
=
F
n
-
1
+
F
n
-
2
for
n
≥
2
.
Let
2
≤
m
≤
n
and
b
=
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
.
In this study, we show that if
F
m
F
n
is a repdigit in base
b
and has at least two digits, then
F
m
F
n
∈
3
,
4
,
5
,
6
,
8
,
9
,
10
,
13
,
15
,
16
,
21
,
24
,
26
,
40
,
42
,
63
,
170
,
273
.
Furthermore, it is shown that if
F
n
is a repdigit in base
b
and has at least two digits, then
(
n
,
b
)
=
(
7
,
3
)
,
(
8
,
4
)
,
(
8
,
6
)
,
(
4
,
2
)
,
(
5
,
4
)
,
(
6
,
3
)
,
(
6
,
7
)
. |
|---|---|
| ISSN: | 0019-5588 0975-7465 |
| DOI: | 10.1007/s13226-021-00041-8 |