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 |
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| container_title | Indian journal of pure and applied mathematics |
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| creator | Erduvan, Fatih Keskin, Refik Şiar, Zafer |
| description | 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
)
. |
| doi_str_mv | 10.1007/s13226-021-00041-8 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2612761613</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2612761613</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-e5dbc1779dd7538e82e6266d9bdca366a5eb0008b1e67dfcb74597b7dce773b63</originalsourceid><addsrcrecordid>eNp9kEtLBDEQhIMouK7-AU8Bz9E8JunkKIurwoIgeg55zTKLO7MmM4j_3ugI3jx101RVFx9Cl4xeM0rhpjDBuSKUM0IpbRjRR2hBDUgCjZLHdafMECm1PkVnpewoVYIas0DyOR1it-3Ggr0rCXvsCj7kIU6hnoYWjx8DXnd-6F0IHe6nvU-5nKOT1r2VdPE7l-h1ffeyeiCbp_vH1e2GBMHMSJKMPjAAEyNIoZPmSXGlovExOKGUk8nXutqzpCC2wUMjDXiIIQEIr8QSXc25tdH7lMpod8OU-_rScsU4KKaYqCo-q0IeSsmptYfc7V3-tIzabzx2xmMrHvuDx-pqErOpVHG_Tfkv-h_XF1KxZvs</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2612761613</pqid></control><display><type>article</type><title>Repdigits base b as products of two Fibonacci numbers</title><source>SpringerLink Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Erduvan, Fatih ; Keskin, Refik ; Şiar, Zafer</creator><creatorcontrib>Erduvan, Fatih ; Keskin, Refik ; Şiar, Zafer</creatorcontrib><description>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
)
.</description><identifier>ISSN: 0019-5588</identifier><identifier>EISSN: 0975-7465</identifier><identifier>DOI: 10.1007/s13226-021-00041-8</identifier><language>eng</language><publisher>New Delhi: Indian National Science Academy</publisher><subject>Applications of Mathematics ; Digits ; Fibonacci numbers ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Original Research</subject><ispartof>Indian journal of pure and applied mathematics, 2021-09, Vol.52 (3), p.861-868</ispartof><rights>The Indian National Science Academy 2021</rights><rights>The Indian National Science Academy 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e5dbc1779dd7538e82e6266d9bdca366a5eb0008b1e67dfcb74597b7dce773b63</citedby><cites>FETCH-LOGICAL-c319t-e5dbc1779dd7538e82e6266d9bdca366a5eb0008b1e67dfcb74597b7dce773b63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13226-021-00041-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13226-021-00041-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Erduvan, Fatih</creatorcontrib><creatorcontrib>Keskin, Refik</creatorcontrib><creatorcontrib>Şiar, Zafer</creatorcontrib><title>Repdigits base b as products of two Fibonacci numbers</title><title>Indian journal of pure and applied mathematics</title><addtitle>Indian J Pure Appl Math</addtitle><description>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
)
.</description><subject>Applications of Mathematics</subject><subject>Digits</subject><subject>Fibonacci numbers</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Original Research</subject><issn>0019-5588</issn><issn>0975-7465</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLBDEQhIMouK7-AU8Bz9E8JunkKIurwoIgeg55zTKLO7MmM4j_3ugI3jx101RVFx9Cl4xeM0rhpjDBuSKUM0IpbRjRR2hBDUgCjZLHdafMECm1PkVnpewoVYIas0DyOR1it-3Ggr0rCXvsCj7kIU6hnoYWjx8DXnd-6F0IHe6nvU-5nKOT1r2VdPE7l-h1ffeyeiCbp_vH1e2GBMHMSJKMPjAAEyNIoZPmSXGlovExOKGUk8nXutqzpCC2wUMjDXiIIQEIr8QSXc25tdH7lMpod8OU-_rScsU4KKaYqCo-q0IeSsmptYfc7V3-tIzabzx2xmMrHvuDx-pqErOpVHG_Tfkv-h_XF1KxZvs</recordid><startdate>20210901</startdate><enddate>20210901</enddate><creator>Erduvan, Fatih</creator><creator>Keskin, Refik</creator><creator>Şiar, Zafer</creator><general>Indian National Science Academy</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210901</creationdate><title>Repdigits base b as products of two Fibonacci numbers</title><author>Erduvan, Fatih ; Keskin, Refik ; Şiar, Zafer</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-e5dbc1779dd7538e82e6266d9bdca366a5eb0008b1e67dfcb74597b7dce773b63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applications of Mathematics</topic><topic>Digits</topic><topic>Fibonacci numbers</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Original Research</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Erduvan, Fatih</creatorcontrib><creatorcontrib>Keskin, Refik</creatorcontrib><creatorcontrib>Şiar, Zafer</creatorcontrib><collection>CrossRef</collection><jtitle>Indian journal of pure and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Erduvan, Fatih</au><au>Keskin, Refik</au><au>Şiar, Zafer</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Repdigits base b as products of two Fibonacci numbers</atitle><jtitle>Indian journal of pure and applied mathematics</jtitle><stitle>Indian J Pure Appl Math</stitle><date>2021-09-01</date><risdate>2021</risdate><volume>52</volume><issue>3</issue><spage>861</spage><epage>868</epage><pages>861-868</pages><issn>0019-5588</issn><eissn>0975-7465</eissn><abstract>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
)
.</abstract><cop>New Delhi</cop><pub>Indian National Science Academy</pub><doi>10.1007/s13226-021-00041-8</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0019-5588 |
| ispartof | Indian journal of pure and applied mathematics, 2021-09, Vol.52 (3), p.861-868 |
| issn | 0019-5588 0975-7465 |
| language | eng |
| recordid | cdi_proquest_journals_2612761613 |
| source | SpringerLink Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Applications of Mathematics Digits Fibonacci numbers Mathematics Mathematics and Statistics Numerical Analysis Original Research |
| title | Repdigits base b as products of two Fibonacci numbers |
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