On the Congruent Number Problem

Peng Tsu Ann
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Peng Tsu Ann: National University of Singapore Kent Ridge, Department of Mathematics

A chapter in International Symposium in Memory of Hua Loo Keng, 1991, pp 231-234 from Springer

Abstract: Abstract Let A be a square—free positive integer. Suppose that A is a congruent number, i.e., suppose that there exist positive rational numbers X, Y, Z such that % MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGyb % WaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaamywamaaCaaaleqabaGa % aGOmaaaakiabg2da9iaadQfadaahaaWcbeqaaiaaikdaaaGccaGGSa % aabaWaaSaaaeaacaaIXaaabaGaaGOmaaaacaWGybGaamywaiabg2da % 9iaadgeacaGGUaaaaaa!43C7! $$\begin{gathered} {X^2} + {Y^2} = {Z^2}, \hfill \\ \frac{1}{2}XY = A. \hfill \\ \end{gathered} $$

Date: 1991
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DOI: 10.1007/978-3-662-07981-2_13

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