On an equation of Goormaghtigh

 Access to full text

 Full (PDF)

1. [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62. Zbl0788.11026
2. [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. Zbl0425.10020
3. [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. Zbl0121.28403
4. [4] R. Goormaghtigh, L'Intermédiaire des Mathématiciens 24 (1917), 88. 
5. [5] T. Nagell, The diophantine equation $x²+7=2^n$, Ark. Mat. 4 (1961), 185-187. Zbl0103.03001
6. [6] S. Ramanujan, Question 464, J. Indian Math. Soc. 5 (1913), Collected Papers, Cambridge Univ. Press, 1927, 327. 
7. [7] C. Runge, Ueber ganzzahlige Los̈ungen von Gleichungen zwischen zwei Veränderlichen, J. Reine Angew. Math. 100 (1887), 425-435. 
8. [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. Zbl0757.11011
9. [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. Zbl0575.10011
10. [10] T. N. Shorey, Integers with identical digits, Acta Arith. 53 (1989), 187-205. Zbl0693.10008
11. [11] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, 1986. Zbl0606.10011
12. [12] C. L. Siegel, Ueber einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1 (1929), 70 pp. Zbl56.0180.05