On the diophantine equation $(x^m-1)/(x-1) = y^n$

• Autorzy: Li Yu , Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 73
• Numer: 4
• Strony: 363-366

Daty

wydano

1995

otrzymano

1994-07-18

poprawiono

1995-04-21

Twórcy

autor

Li Yu

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

autor

Maohua Le

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

Bibliografia

• [1] H. Edgar, Problems and some results concerning the diophantine equation $1 + A + A²+ ... + A^{x-1} = P^y$, Rocky Mountain J. Math. 15 (1985), 327-329.
• [2] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1981.
• [3] K. Inkeri, On the diophantine equation $a(x^m - 1)/(x - 1) = y^n$, Acta Arith. 21 (1972), 299-311.
• [4] M.-H. Le, A note on the diophantine equation $(x^m - 1)/(x - 1) = y^n$, Acta Arith. 64 (1993), 19-28.
• [5] M.-H. Le, A note on perfect powers of the form $x^{m-1} + ... + x + 1$, Acta Arith. 69 (1995), 91-98.
• [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. Obláth, Une propriété des puissances parfaites, Mathesis 65 (1956), 356-364.
• [8] W.-J. Shi, On K₄ simple groups, Kexue Tongbao 36 (1991), 1281-1283 (in Chinese).
• [9] T. Shorey and R. Tijdeman, New applications of diophantine approximations to diophantine equations, Math. Scand. 39 (1976), 5-18.
• [10] T. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Univ. Press, 1986.