Alfred Jacobus Van Der Poorten
Abstract
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We generalise remarks of Euler and of Perron by explaining how to detail all quadratic irrational integers for which the symmetric part of the period of their continued fraction expansion commences with prescribed partial quotients. The function field case is particularly striking.
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We generalise remarks of Euler and of Perron by explaining how to detail all quadratic irrational integers for which the symmetric part of the period of their continued fraction expansion commences with prescribed partial quotients. The function field case is particularly striking.
Key concepts: Continued fraction, Irrational number, Mathematics, Fraction (chemistry), Quadratic equation, Euler's formula, Quotient, Quadratic field