On an equation of Goormaghtigh

• Autorzy: Yu. V. Nesterenko , T. N. Shorey
• Języki publikacji: EN

Kategorie tematyczne

• 11D61: Exponential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 83
• Numer: 4
• Strony: 381-389

Daty

wydano

1998

otrzymano

1997-03-24

poprawiono

1997-09-22

Twórcy

autor

Yu. V. Nesterenko

• Department of Mathematics, Moscow State University, Moscow 119899, Russia

autor

T. N. Shorey

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

Bibliografia

• [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
• [2] R. Balasubramanian and T. N. Shorey, On the equation $a(x^m-1)/(x-1) = b(y^n-1)/(y-1)$, Math. Scand. 46 (1980), 177-182.
• [3] H. Davenport, D. J. Lewis and A. Schinzel, Equations of the form f(x) = g(y), Quart. J. Math. Oxford Ser. (2) 12 (1961), 304-312.
• [4] R. Goormaghtigh, L'Intermédiaire des Mathématiciens 24 (1917), 88.
• [5] T. Nagell, The diophantine equation $x²+7 = 2^n$, Ark. Mat. 4 (1961), 185-187.
• [6] S. Ramanujan, Question 464, J. Indian Math. Soc. 5 (1913), Collected Papers, Cambridge Univ. Press, 1927, 327.
• [7] C. Runge, Ueber ganzzahlige Los̈ungen von Gleichungen zwischen zwei Veränderlichen, J. Reine Angew. Math. 100 (1887), 425-435.
• [8] N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk), Indag. Math. (N.S.) 3 (1992), 79-90.
• [9] T. N. Shorey, On the equation $a(x^m-1)/(x-1) = b(y^n-1)/(y-1)$ (II), Hardy-Ramanujan J. 7 (1984), 1-10.
• [10] T. N. Shorey, Integers with identical digits, Acta Arith. 53 (1989), 187-205.
• [11] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, 1986.
• [12] C. L. Siegel, Ueber einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1 (1929), 70 pp.