A note on the Diophantine equation px(2) + q(2n) = y(p)

作者：Wang Xiaoying^*; Zhang Han

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2017, 60(1): 51-57.

• exponential diophantine equation
• class number of binary quadratic forms
• primitive divisor of Lehmer numbers

Let p, q be odd primes such that p equivalent to 1( mod 4) and p not equal q. In this paper, we prove that if q < 4p - 1 or q < 149, then the equation px(2) + q(2n) = y(P) has no positive integer solutions (x, y, n) with gcd(x, y) = 1.

• 出版日期2017
• 单位西北大学