On the diophantine equation $D₁x² + D₂ = 2^{n+2}$

• Autorzy: Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 64
• Numer: 1
• Strony: 29-41

Daty

wydano

1993

otrzymano

1992-01-23

poprawiono

1992-10-28

Twórcy

autor

Maohua Le

• Research Department, Changsha Railway Institute, Changsha, Hunan, P. R. China

Bibliografia

• [1] R. Apéry, Sur une équation diophantienne, C. R. Acad. Sci. Paris Sér. A 251 (1960), 1263-1264.
• [2] A. Baker, Contribution to the theory of diophantine equations I: On the representation of integers by binary forms, Philos. Trans. Roy. Soc. London Ser. A 263 (1967), 273-297.
• [3] V. I. Baulin, On an indeterminate equation of the third degree with least positive discriminant, Tul'sk. Gos. Ped. Inst. Uchen. Zap. Fiz.-Mat. Nauk Vyp. 7 (1960), 138-170 (in Russian).
• [4] E. Bender and N. Herzberg, Some diophantine equations related to the quadratic form ax²+by², in: Studies in Algebra and Number Theory, G.-C. Rota (ed.), Adv. in Math. Suppl. Stud. 6, Academic Press, San Diego 1979, 219-272.
• [5] F. Beukers, On the generalized Ramanujan-Nagell equation I, Acta Arith. 38 (1981), 389-410.
• [6] J. H. E. Cohn, On square Fibonacci numbers, J. London Math. Soc. 39 (1964), 537-540.
• [7] K. Győry and Z. Z. Papp, Norm form equations and explicit lower bounds for linear forms with algebraic coefficients, in: Studies in Pure Mathematics, Akadémiai Kiadó, Budapest 1983, 245-257.
• [8] M.-H. Le, The divisibility of the class number for a class of imaginary quadratic fields, Kexue Tongbao (Chinese) 32 (1987), 724-727 (in Chinese).
• [9] M.-H. Le, On the number of solutions of the generalized Ramanujan-Nagell equation $x²-D = 2^n+2$, Acta Arith. 60 (1991), 149-167.
• [10] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, Mass., 1983.
• [11] M. Mignotte and M. Waldschmidt, Linear forms in two logarithms and Schneider's method III, Ann. Fac. Sci. Toulouse 97 (1989), 43-75.
• [12] T. Nagell, The diophantine equation $x²+7 = 2^n$, Ark. Mat. 4 (1960), 185-187