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\rightline{KA-TP-07-2004} \psn
\rightline{September 2004}
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\centerline{ \bf Chebyshev Polynomials and Certain Quadratic Diophantine Equations}\psn
\centerline{Wolfdieter L a n g}\psn 
\centerline{\it {Institut f\"ur Theoretische Physik}}\psn  
\centerline{\it{ Universit\"at Karlsruhe} }\pn
\centerline{\it {Kaiserstrasse 12, D-76128 Karlsruhe,}}\pn
\centerline{\it{Germany}}
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Classes of binary quadratic diophantine equations (including the standard types of {\sl Pell} equations) which follow from the well-known {\sl Cassini-}{\sl Simson-}identity for {\sl Chebyshev}'s polynomials of the second kind are derived and their solutions are discussed.  
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AMS MSC numbers: 11D05, 11B83, 33C45    
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$^{*}$ E-mail: wolfdieter.lang@physik.uni-karlsruhe.de, \pn 
http://www-itp.physik.uni-karlsruhe.de/${\ \tilde{}}\ $wl 
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