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Die Anzahl von Lösungen gewisser diophantischer Gleichungen. (German) Zbl 0079.27101


MSC:

11D45 Counting solutions of Diophantine equations
11D41 Higher degree equations; Fermat’s equation
11D61 Exponential Diophantine equations

Citations:

Zbl 0034.17003
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Full Text: DOI

References:

[1] T. Nagell, Des équations indéterminéesx 2 +x+1=y n etx 2 +x+1=3y n . Norsk matem. forenings skrifter I Nr. 2, 1–14 (1921).
[2] T. Nagell, Verallgemeinerung eines Fermatschen Satzes. Arch. Math.5, 153–159 (1954). · Zbl 0055.03608 · doi:10.1007/BF01899332
[3] T. Nagell, Sur l’impossibilité de quelques équations à deux indeterminées. Norsk matem. forenings skrifter I Nr. 13, 65–82 (1923).
[4] T. Nagell, On the Diophantine equationx 2 +8D=y n . Ark. mat.3, 103–112 (1955). · Zbl 0064.04007 · doi:10.1007/BF02589348
[5] T. Nagell, Contributions to the theory of a category of Diophantine equations of the second degree with two unknowns. Nova Acta Soc. Sci. Upsal. IV Ser.16, 1–38 (1955).
[6] W. Ljunggren, Einige Bemerkungen über die Darstellung ganzer Zahlen durch binäre kubische Formen mit positiver Diskriminante. Acta math.75, 1–21 (1942). · Zbl 0060.09104 · doi:10.1007/BF02404100
[7] W. Ljunggren, On the Diophantine equationx 2 +p 2 =y n . Norske Vid. Selsk. Forhdl.16, 27–30 (1943). · Zbl 0060.09106
[8] W. Ljunggren, On the Diophantine equationx 2 +D=y n . Norske Vid. Selsk. Forhdl.17, 93–96 (1944). · Zbl 0060.09107
[9] B. Persson, On a diophantine equation in two unknowns. Ark. mat.1, 45–57 (1949). · Zbl 0034.17003 · doi:10.1007/BF02590466
[10] E.Netto, Lehrbuch der Combinatorik. 2. Aufl. 1927. · JFM 53.0073.09
[11] A. Thue, Über die Unlösbarkeit der Gleichungax 2 +bx+c=dy n in großen ganzen Zahlenx undy. Arch. Math. Naturvid.24, 1–6 (1916).
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