A note on the diophantine equation $(x^m-1)/(x-1) = y^n$

• Autorzy: Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 64
• Numer: 1
• Strony: 19-28

Daty

wydano

1993

otrzymano

1991-09-13

poprawiono

1992-10-28

Twórcy

autor

Maohua Le

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

Bibliografia

• [1] A. Baker, The theory of linear forms in logarithms, in: Transcendence Theory: Advances and Applications, Academic Press, London 1977, 1-27.
• [2] D. Estes, R. Guralnick, M. Schacher and E. Straus, Equations in prime powers, Pacific J. Math. 118 (1985), 359-367.
• [3] W. Feit, Some consequences of classification of finite simple groups, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 175-181.
• [4] R. Guralnick, Subgroups including the same permutation representation, J. Algebra 81 (1983), 312-319.
• [5] L.-K. Hua, Introduction to Number Theory, Springer, Berlin 1982.
• [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] R. Perlis, On the class number of arithmetically equivalent fields, J. Number Theory 10 (1978), 489-509.
• [8] T. Shorey and R. Tijdeman, New applications of diophantine approximations to diophantine equations, Math. Scand. 39 (1976), 5-18.
• [9] C. L. Siegel, Einige Erläuterungen zu Thues Untersuchungen über Annäherungswerte algebraischer Zahlen und diophantische Gleichungen, Nachr. Göttingen Math.-Phys. Kl. II 1970 (8), 169-195.
• [10] J. Turk, On the difference between perfect powers, Acta Arith. 45 (1986), 289-307