A note on the integer solutions ofhyperelliptic equations

• Autorzy: Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1995
• Tom: 68
• Numer: 2
• Strony: 171-177

Daty

wydano

1995

otrzymano

1993-04-26

Twórcy

autor

Maohua Le

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

Bibliografia

• [1] A. Baker, Bounds for the solutions of the hyperelliptic equation, Proc. Cambridge Philos. Soc. 65 (1969), 439-444.
• [2] L.-K. Hua, Introduction to Number Theory, Springer, Berlin, 1982.
• [3] C. Ko, On the diophantine equation $x^2=y^n+1$, xy ≠ 0, Sci. Sinica 14 (1964), 457-460.
• [4] V. A. Lebesgue, Sur l'impossibilité, en nombres entiers, de l'équation $x^m=y^2+1$, Nouv. Ann. Math. (1) 9 (1850), 178-181.
• [5] W. J. LeVeque, On the equation $y^m=f(x)$, Acta Arith. 9 (1964), 209-219.
• [6] W. Ljunggren, Noen setninger om ubestemte likninger av formen $(x^n-1)/(x-1) =y^q$, Norsk. Mat. Tidsskr. 25 (1943), 17-20.
• [7] H. L. Montgomery and R. C. Vaughan, The order of magnitude of mth coefficients of cyclotomic polynomials, Glasgow Math. J. 27 (1985), 143-159.
• [8] J. Riordan, Introduction to Combinatorial Analysis, Wiley, 1958.
• [9] A. Rotkiewicz and W. Złotkowski, On the diophantine equation $1+p^α_1+... ... +p^α_k=y^2$, in: Number Theory, Vol. II (Budapest 1987), North-Holland, Amsterdam, 1990, 917-937.
• [10] V. G. Sprindžuk, Hyperelliptic diophantine equation and class numbers of ideals, Acta Arith. 30 (1976), 95-108 (in Russian).
• [11] P. G. Walsh, A quantitative version of Runge's theorem on diophantine equations, Acta Arith. 62 (1992), 157-172.