丢翻图方程x^2+a^2=2y^n解法的计算研究

SOLUTION TO DIOPHANTINE EQUATION x^2+a^2=2y^n

本文研究了一类丢番图方程的解.利用对Thue方程解的估计和方程解的连分式展开,获得了所求丢番图方程解的个数、解上界的估计和一般的求解算法.最后利用该算法给出了1≤a≤108的所有解.

This article considers a class of Diophantine equations. By the algorithm, we get the number of solutions, upper bounds of the solutions, and the general method to solve the equation. Finally, we give all solutions for 1≤a≤108.