Extension of a parametric family of Diophantine triples in Gaussian integers
We prove that if { k , 4 k + 4 , 9 k + 6 , d } , where k ∈ Z [ i ] , k ≠ 0 , - 1 , is a Diophantine quadruple in the ring of Gaussian integers, then d = 144 k 3 + 240 k 2 + 124 k + 20 .
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| Veröffentlicht in: | Acta mathematica Hungarica 2016-04, Vol.148 (2), p.312-327 |
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| Format: | Artikel |
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| container_issue | 2 |
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| container_title | Acta mathematica Hungarica |
| container_volume | 148 |
| creator | Bayad, A. Filipin, A. Togbé, A. |
| description | We prove that if
{
k
,
4
k
+
4
,
9
k
+
6
,
d
}
, where
k
∈
Z
[
i
]
,
k
≠
0
,
-
1
, is a Diophantine quadruple in the ring of Gaussian integers, then
d
=
144
k
3
+
240
k
2
+
124
k
+
20
. |
| doi_str_mv | 10.1007/s10474-016-0581-6 |
| format | Article |
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{
k
,
4
k
+
4
,
9
k
+
6
,
d
}
, where
k
∈
Z
[
i
]
,
k
≠
0
,
-
1
, is a Diophantine quadruple in the ring of Gaussian integers, then
d
=
144
k
3
+
240
k
2
+
124
k
+
20
.</description><identifier>ISSN: 0236-5294</identifier><identifier>EISSN: 1588-2632</identifier><identifier>DOI: 10.1007/s10474-016-0581-6</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Mathematics ; Mathematics and Statistics ; Number Theory</subject><ispartof>Acta mathematica Hungarica, 2016-04, Vol.148 (2), p.312-327</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2016</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-4b3a515bd9a407abc66695c011b66a8b1af1b2538554e621ec27f653ba4f39b33</citedby><cites>FETCH-LOGICAL-c322t-4b3a515bd9a407abc66695c011b66a8b1af1b2538554e621ec27f653ba4f39b33</cites><orcidid>0000-0002-8003-335X ; 0000-0002-0867-8305</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10474-016-0581-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10474-016-0581-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04463448$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bayad, A.</creatorcontrib><creatorcontrib>Filipin, A.</creatorcontrib><creatorcontrib>Togbé, A.</creatorcontrib><title>Extension of a parametric family of Diophantine triples in Gaussian integers</title><title>Acta mathematica Hungarica</title><addtitle>Acta Math. Hungar</addtitle><description>We prove that if
{
k
,
4
k
+
4
,
9
k
+
6
,
d
}
, where
k
∈
Z
[
i
]
,
k
≠
0
,
-
1
, is a Diophantine quadruple in the ring of Gaussian integers, then
d
=
144
k
3
+
240
k
2
+
124
k
+
20
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><issn>0236-5294</issn><issn>1588-2632</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OwzAQhC0EEqXwANx85WDwf5JjVUpBisQFztY6ONRV6kR2iujb4yiII6ddzc6sNB9Ct4zeM0qLh8SoLCShTBOqSkb0GVowVZaEa8HP0YJyoYnilbxEVyntKaVKULlA9eZ7dCH5PuC-xYAHiHBwY_QNbuHgu9MkP_p-2EEYfXA4n4bOJewD3sIxJQ8h76P7dDFdo4sWuuRufucSvT9t3tbPpH7dvqxXNWkE5yORVoBiyn5UIGkBttFaV6qhjFmtobQMWma5EqVS0mnOXMOLVithQbaiskIs0d38dwedGaI_QDyZHrx5XtVm0qiUWkhZfrHsZbO3iX1K0bV_AUbNhM7M6ExGZyZ0RucMnzMpe0NuZvb9MYZc6Z_QD1eLcIo</recordid><startdate>20160401</startdate><enddate>20160401</enddate><creator>Bayad, A.</creator><creator>Filipin, A.</creator><creator>Togbé, A.</creator><general>Springer Netherlands</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-8003-335X</orcidid><orcidid>https://orcid.org/0000-0002-0867-8305</orcidid></search><sort><creationdate>20160401</creationdate><title>Extension of a parametric family of Diophantine triples in Gaussian integers</title><author>Bayad, A. ; Filipin, A. ; Togbé, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-4b3a515bd9a407abc66695c011b66a8b1af1b2538554e621ec27f653ba4f39b33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bayad, A.</creatorcontrib><creatorcontrib>Filipin, A.</creatorcontrib><creatorcontrib>Togbé, A.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Acta mathematica Hungarica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bayad, A.</au><au>Filipin, A.</au><au>Togbé, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extension of a parametric family of Diophantine triples in Gaussian integers</atitle><jtitle>Acta mathematica Hungarica</jtitle><stitle>Acta Math. Hungar</stitle><date>2016-04-01</date><risdate>2016</risdate><volume>148</volume><issue>2</issue><spage>312</spage><epage>327</epage><pages>312-327</pages><issn>0236-5294</issn><eissn>1588-2632</eissn><abstract>We prove that if
{
k
,
4
k
+
4
,
9
k
+
6
,
d
}
, where
k
∈
Z
[
i
]
,
k
≠
0
,
-
1
, is a Diophantine quadruple in the ring of Gaussian integers, then
d
=
144
k
3
+
240
k
2
+
124
k
+
20
.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10474-016-0581-6</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-8003-335X</orcidid><orcidid>https://orcid.org/0000-0002-0867-8305</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0236-5294 |
| ispartof | Acta mathematica Hungarica, 2016-04, Vol.148 (2), p.312-327 |
| issn | 0236-5294 1588-2632 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_04463448v1 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Mathematics Mathematics and Statistics Number Theory |
| title | Extension of a parametric family of Diophantine triples in Gaussian integers |
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