A note on perfect powers of the form $x^{m-1} + ... + x + 1$

• Autorzy: Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 1
• Strony: 91-98

Daty

wydano

1995

otrzymano

1994-01-12

poprawiono

1994-05-01

Twórcy

autor

Maohua Le

• Department of Mathematics, Zhanjiang Teacher's College, P.O. Box 524048, Zhanjiang, Guangdong, P.R. China

Bibliografia

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• [2] A. Baker, Rational approximations to ∛2 and other algebraic numbers, Quart. J. Math. Oxford 15 (1964), 375-383.
• [3] W. F. H. Berwick, Integral Bases, Cambridge Univ. Press, 1927.
• [4] J. W. S. Cassels, On the equation $a^x - b^y = 1$, II, Math. Proc. Cambridge Philos. Soc. 56 (1960), 97-103.
• [5] L.-K. Hua, Introduction to Number Theory, Springer, Berlin, 1982.
• [6] S. Lang, Algebraic Number Theory, Addison-Wesley, Reading, Massachusetts, 1970.
• [7] M.-H. Le, A note on the equation $(x^m-1)/(x-1) = y^n + 1$, Math. Proc. Cambridge Philos. Soc. 115 (1994), to appear.
• [8] W. Ljunggren, Noen setninger om ubestemte likninger av formen $(x^n-1)/(x-1) = y^q$, Norsk Mat. Tidsskr. 25 (1943), 17-20.
• [9] W. Ljunggren, On an improvement of a theorem of T. Nagell concerning the diophantine equation Ax³ + By³ = C, Math. Scand. 1 (1953), 297-309.
• [10] T. N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Cambridge Philos. Soc. 99 (1986), 195-207.
• [11] T. N. Shorey, On the equation $z^q = (x^n-1)/(x-1)$, Indag. Math. 48 (1986), 345-351.
• [12] C. L. Siegel, Die Gleichung $ax^n - by^n = c$, Math. Ann. 144 (1937), 57-68.