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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{ Universit\"at Karlsruhe} \psn
\centerline{D-76128 Karlsruhe, Germany}\psn 
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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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