<?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>S0034-74262019000100001</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Pillai's problem with Padovan numbers and powers of two]]></article-title>
<article-title xml:lang="es"><![CDATA[El problema de Pillai con números de Padovan y potencias de dos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[GARCÍA LOMELI]]></surname>
<given-names><![CDATA[ANA CECILIA]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[HERNÁNDEZ HERNÁNDEZ]]></surname>
<given-names><![CDATA[SANTOS]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Zacatecas  ]]></institution>
<addr-line><![CDATA[Zacatecas ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Zacatecas  ]]></institution>
<addr-line><![CDATA[Zacatecas ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<volume>53</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>14</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262019000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262019000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262019000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT. Let (P  n ) n&#8805;0 be the Padovan sequence given by P 0 = 0, P 1 = P 2 = 1 and the recurrence formula P n+3 = P  n+1 + P n for all n &#8805; 0. In this note we study and completely solve the Diophantine equation P n - 2 m = P n1 -2 m1 in non-negative integers (n,m,n  1 ,m  1 ).]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN. Sea (P  n ) n&#8805;0 la sucesión de Padovan dada mediante P 0 = 0, P 1 = P 2 = 1 y la fórmula de recurrencia P n+3 = P  n+1 + P n para todo n &#8805; 0. En esta nota estudiamos y resolvemos completamente la ecuación diofántica P n - 2 m = P n1 -2 m1 en enteros no negativos (n,m,n  1 ,m  1 ).]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Padovan sequence]]></kwd>
<kwd lng="en"><![CDATA[Pillai's problem]]></kwd>
<kwd lng="en"><![CDATA[linear forms in logarithms]]></kwd>
<kwd lng="en"><![CDATA[reduction method]]></kwd>
<kwd lng="es"><![CDATA[Sucesión de Padovan]]></kwd>
<kwd lng="es"><![CDATA[Problema de Pillai]]></kwd>
<kwd lng="es"><![CDATA[Formas lineales en logaritmos]]></kwd>
<kwd lng="es"><![CDATA[método de reducción]]></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[Davenport]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
<name>
<surname><![CDATA[Baker]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The equations 3X2 - 2 = Y2 and 8X2 - 7 = Z2, Quart]]></article-title>
<source><![CDATA[J. Math. Oxford]]></source>
<year>1969</year>
<volume>20</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>129-37</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[J. J]]></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[Powers of two as sums of two k-Fibonacci numbers]]></article-title>
<source><![CDATA[Miskolc Math. Notes]]></source>
<year>2016</year>
<volume>17</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>85-100</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[Bravo]]></surname>
<given-names><![CDATA[J. J]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
<name>
<surname><![CDATA[Yazan]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Pillai's problem with Tribonacci numbers and Powers of 2, Bull]]></article-title>
<source><![CDATA[Korean Math. Soc]]></source>
<year>2017</year>
<volume>54</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>1069-80</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[Bugeaud]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
<name>
<surname><![CDATA[Mignotte]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Siksek]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Classical and modular approaches to exponential diophantine equations I: Fibonacci and Lucas perfect powers]]></article-title>
<source><![CDATA[Ann. of Math]]></source>
<year>2006</year>
<volume>163</volume>
<page-range>969-1018</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[Chim]]></surname>
<given-names><![CDATA[K. C]]></given-names>
</name>
<name>
<surname><![CDATA[Pink]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
<name>
<surname><![CDATA[Ziegler]]></surname>
<given-names><![CDATA[V]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On a variant of Pillai's problem]]></article-title>
<source><![CDATA[Int. J. Number Theory]]></source>
<year>2017</year>
<volume>7</volume>
<page-range>1711-27</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[Chim]]></surname>
<given-names><![CDATA[K. C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On a variant of Pillai's problem II]]></article-title>
<source><![CDATA[J. Number Theory]]></source>
<year>2018</year>
<volume>183</volume>
<page-range>269-90</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[Ddamulira]]></surname>
<given-names><![CDATA[M]]></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[On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2]]></article-title>
<source><![CDATA[Monatsh. Math]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ddamulira]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
<name>
<surname><![CDATA[Rakotomalala]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On a problem of Pillai with Fibonacci and powers of2]]></article-title>
<source><![CDATA[Proc. Indian Acad. Sci. (Math. Sci.)]]></source>
<year>2017</year>
<volume>127</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>411-21</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dujella]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Petho]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A generalization of a theorem of Baker and Davenport]]></article-title>
<source><![CDATA[Quart. J. Math. Oxford]]></source>
<year>1998</year>
<volume>49</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>291-306</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hernandez Hernández]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
<name>
<surname><![CDATA[Rivera]]></surname>
<given-names><![CDATA[L. M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Pillai's problem with the Fibonacci and Pell sequences]]></article-title>
<source><![CDATA[Accepted in the Bol. Soc. Mat. Mexicana]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herschfeld]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The equation 2x-3y = d]]></article-title>
<source><![CDATA[Bull. Amer. Math. Soc]]></source>
<year>1936</year>
<volume>42</volume>
<page-range>231-4</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Matveev]]></surname>
<given-names><![CDATA[E. M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An explicit lower bound for a homogeneous rational linear form in the logarithms ofalgebraic numbers II]]></article-title>
<source><![CDATA[Izv. Math]]></source>
<year>2000</year>
<volume>64</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1217-69</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pillai]]></surname>
<given-names><![CDATA[S. S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On ax - by = c, J]]></article-title>
<source><![CDATA[Indian Math. Soc]]></source>
<year>1936</year>
<volume>2</volume>
<page-range>119-22</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pillai]]></surname>
<given-names><![CDATA[S. S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the equation 2x - 3y = 2X +3Y]]></article-title>
<source><![CDATA[Bull. Calcutta Math. Soc]]></source>
<year>1945</year>
<volume>37</volume>
<page-range>15-20</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guzman Sanchez]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Luca]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Linear combinations of factorials and S-units in a binary recurrence sequence]]></article-title>
<source><![CDATA[Ann. Math. Quebec]]></source>
<year>2014</year>
<volume>38</volume>
<page-range>169-88</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sloane]]></surname>
<given-names><![CDATA[N. J. A]]></given-names>
</name>
</person-group>
<source><![CDATA[The On-Line Encyclopedia of Integer Sequences]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stroeker]]></surname>
<given-names><![CDATA[R. J]]></given-names>
</name>
<name>
<surname><![CDATA[Tijdeman]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Diophantine equations, Computational methods in number theory]]></article-title>
<source><![CDATA[Math. Centre Tracts]]></source>
<year>1982</year>
<numero>155</numero>
<issue>155</issue>
<page-range>321-69</page-range><publisher-loc><![CDATA[Amsterdan ]]></publisher-loc>
<publisher-name><![CDATA[Centre for Mathematics and Computer Science]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
