<?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>S0034-74262006000200002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[PALINDROMIC POWERS]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández Hernández]]></surname>
<given-names><![CDATA[Santos]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Florian Luca]]></surname>
<given-names><![CDATA[Santigo]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Pontificia Universidad Católica de Chile Facultad de Matemáticas ]]></institution>
<addr-line><![CDATA[Santiago Vicuña Mackenna]]></addr-line>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[Morelia Michoacán]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2006</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2006</year>
</pub-date>
<volume>40</volume>
<numero>2</numero>
<fpage>81</fpage>
<lpage>86</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262006000200002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262006000200002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262006000200002&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this paper, given an integer a > 1, we look at the smallest exponent n such that an is not a palindrome.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este artículo, dado un entero a > 1, nosotros estudiamos el menor exponente n tal que a n no sea palindromo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Palindromes]]></kwd>
<kwd lng="en"><![CDATA[Applications of Baker's method]]></kwd>
<kwd lng="en"><![CDATA[Discrepancy]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face=verdana>      <p> <font size="4">       <center>    <b>PALINDROMIC POWERS </b>   </center>  </font></p>     <p>&nbsp;</p> </font>     <p><font size="2" face="verdana"><b>Santos Hern&aacute;ndez Hern&aacute;ndez*, Santigo Florian Luca**</b></font></p>  <font size="2" face=verdana>     <p>* Pontificia Universidad Cat&oacute;lica de Chile,    Santiago</p>     <p>Facultad de Matem&aacute;ticas, Vicu&ntilde;a    Mackenna 4860</p>     <p>e-mail: <a href="mailto:shernand@mat.puc.cl">shernand@mat.puc.cl</a></p>     <p>** Universidad Nacional Aut&oacute;noma de M&eacute;xico, M&eacute;xico D. F.</p>     <p>Instituto de Matem&aacute;ticas C.P. 58089, Morelia, Michoac&aacute;n, M&eacute;xico</p>     ]]></body>
<body><![CDATA[<p>e-mail: <a href="mailto:fluca@matmor.unam.mx">fluca@matmor.unam.mx</a></p>     <p>&nbsp;</p> <hr size="2">     <p>&nbsp;</p>     <p><b>Abstract.</b> In this paper, given an integer a &gt; 1, we look at the smallest    exponent n such that an is not a palindrome. </p>     <p><i><b>Keywords and phrases.</b></i> Palindromes, Applications of Baker's method,    Discrepancy. </p>     <p><i>2000 Mathematics Subject Classification. Primary: 11D75. Secondary: 11J25,    11J71, 11J86. </i></p>  <hr size="1">      <p><b>Resumen.</b> En este art&iacute;culo, dado un entero <i>a</i> &gt; 1, nosotros    estudiamos el menor exponente <i>n</i> tal que <i>a<sup>n</sup></i> no sea <i>palindromo</i>. </p>   <hr size="2">     <p>FULL TEXT IN <a href="pdf/rcm/v40n2/v40n2a02.pdf">PDF</a></p>  <hr size="2">     <p>    <center><b>References</b></center></p>     ]]></body>
<body><![CDATA[<!-- ref --><p> [1] W. D. Banks, D. N. Hart &amp; M. Sakata, Almost all palindromes are composite,    <i>Math. Res. Lett.</i> 11 (2004), 853-868. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0034-7426200600020000200001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>[2] M. Harminic &amp; R. Sot&aacute;k, Palindromic numbers in arithmetic progressions,    <i>Fibonacci Quart.</i> 36 (1998), 259-261. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000024&pid=S0034-7426200600020000200002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>[3] I. Korec, Palindromic squares for various number system bases, <i>Math. Slovaca </i>41 (1991), 261-276. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000025&pid=S0034-7426200600020000200003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>[4] L. Kuipers &amp; H. Niederreiter, <i>Uniform Distribution of Sequences</i>, Wiley-    Interscience, New-York, 1974. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000026&pid=S0034-7426200600020000200004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>[5] F. Luca, Palindromes in Lucas sequences, <i>Monatsh. Math.</i> 138 (2003), 209-223.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000027&pid=S0034-7426200600020000200005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>[6] E. M. Matveev, An explicit lower bound for a homogeneous rational linear    form in logarithms of algebraic numbers II, <i>Izv. Ross. Akad. Nauk. Ser. Math.</i>  64 (2000), 125-180; English translation Izv. Math. 64 (2000), 1217-1269. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000028&pid=S0034-7426200600020000200006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>[7] J. Rivat &amp; G. Tenenbaum, Constantes d'Erd&ouml;s-Tur&aacute;n, <i>Ramanujan    J.</i> 9 (2005), 111-121. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000029&pid=S0034-7426200600020000200007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p>(Recibido en mayo de 2006. Aceptado en julio de 2006) </p>      <p>&nbsp; </p> </font>      ]]></body><back>
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