<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262022000200179</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v56n2.108374</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Upper bound on the solution to F (2k) n = (F (2k) m with negative subscripts]]></article-title>
<article-title xml:lang="es"><![CDATA[Cotas superiores de las soluciones de F (2k) n = (F (2k) m con subíndices negativos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Peth&#337;]]></surname>
<given-names><![CDATA[Attila]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Szalay]]></surname>
<given-names><![CDATA[László]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University of Debrecen  ]]></institution>
<addr-line><![CDATA[Debrecen ]]></addr-line>
<country>Hungary</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,J. Selye University  ]]></institution>
<addr-line><![CDATA[Komárno ]]></addr-line>
<country>Slovakia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,University of Sopron  ]]></institution>
<addr-line><![CDATA[Sopron ]]></addr-line>
<country>Hungary</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>56</volume>
<numero>2</numero>
<fpage>179</fpage>
<lpage>187</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262022000200179&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262022000200179&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262022000200179&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper, we provide an explicit upper bound on the absolute value of the solutions n &lt; m &lt; 0 to the Diophantine equation F  (k)  n = ±F  (k)  m , assuming k is even. Here {F  (k)  n } n &#8712; Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo presentamos una cota superior explícita para el valor absoluto de las soluciones con n &lt; m &lt; 0 de la ecuación Diofantina F  (k)  n = ±F  (k)  m , bajo la hipótesis que k es par. En la ecuación anterior {F  (k)  n } n &#8712; Z denota la sucesión de Fibonacci k-generalizada. La cota superior sólo depende de k.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[k-generalized Fibonacci sequence]]></kwd>
<kwd lng="en"><![CDATA[total multiplicity]]></kwd>
<kwd lng="es"><![CDATA[sucesiones de Fibonacci k-generalizadas]]></kwd>
<kwd lng="es"><![CDATA[multiplicidad total]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bravo]]></surname>
<given-names><![CDATA[E. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Total multiplicity of the Tribonacci sequence]]></article-title>
<source><![CDATA[Colloq. Math]]></source>
<year>2020</year>
<volume>159</volume>
<page-range>71-6</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bravo]]></surname>
<given-names><![CDATA[E. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Togbé]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Kafle]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On a conjecture about total multiplicity of Tribonacci sequence]]></article-title>
<source><![CDATA[Colloq. Math]]></source>
<year>2020</year>
<volume>159</volume>
<page-range>61-9</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dresden]]></surname>
<given-names><![CDATA[G. P. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Du]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A simplified Binet formula for k-generalized Fibonacci numbers]]></article-title>
<source><![CDATA[J. Integer Seq]]></source>
<year>2014</year>
<volume>17</volume>
<page-range>9</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dubickas]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the distance between two algebraic numbers]]></article-title>
<source><![CDATA[Bull. Malays. Math. Sci. Soc]]></source>
<year>2020</year>
<volume>43</volume>
<page-range>3049-64</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the zero-multiplicity of a fifth-order linear recurrence]]></article-title>
<source><![CDATA[Int. J. Number Theor]]></source>
<year>2019</year>
<volume>15</volume>
<page-range>585-95</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Peth&#337;]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the k-generalized Fibonacci numbers with negative indices]]></article-title>
<source><![CDATA[Publ. Math. Debrecen]]></source>
<year>2021</year>
<volume>98</volume>
<page-range>401-18</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wolfram]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Solving generalized Fibonacci recurrences]]></article-title>
<source><![CDATA[Fibonacci Quart]]></source>
<year>1988</year>
<volume>36</volume>
<page-range>129-45</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
