Two diophantine systems

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1976 Germany English Publisher:Springer Science and Business Media LLCJournal:Manuscripta Mathematica, volume 18, pages 337-341 (issn: 0025-2611, eissn: 1432-1785,

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Authors: Moessner, Alfred; Xeroudakes, George;

doi: 10.1007/bf01270494

Two diophantine systems

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Abstract

Die Verff. geben eine Methode an zur Lösbarkeit der folgenden zwei diophantischen Systeme \[ A,B,C \overset{n}{=} D,E \quad (n=2,4), \quad A-B = D-E \tag{1} \] und \[ A_1, A_2,A_3,A_4 \overset{n}{=} B_1,B_1,B_2,B_2\quad (n=2,4), \quad A_1A_2A_3A_4 = B_1^2B_2^2. \tag{2}\] Hierbei bedeutet die Teilung der zwei Zahlmengen durch das Symbol \(\overset{n}{=}\), daß sie dieselben Summen von \(n\)-ten Potenzen für die angegebenen Werte von \(n\) haben.

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Germany

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DigiZeitschriften
Germany

Keywords

510.mathematics, Linear Diophantine equations, Cubic and quartic Diophantine equations, Article, Diophantine equations in many variables

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