A note on the Diophantine equation (x(p)-1)/(x-1) = p(e)y(q)

作者：Han Di^*; Guan Wenji

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2014, 57(1): 35-43.

• Higher diophantine equation
• Nagell-Ljunggren equation
• Gel'fond-Baker method

Let p, q be odd primes, and let e is an element of {0,1}. In this paper, using a lower bound for two logarithms in the complex case, we prove that if p equivalent to 3 (mod4) and q > 220p(log p)(2), then the equation (x(p) - 1)/(x - 1) = p(e)y(q) has no positive integer solution (x, y) with min{x,y} > 1.

• 出版日期2014
• 单位西北大学