关于丢番图方程a^m-kb^n=2和a^m-lb^n=1

ON THE DIOPHANTINE EQUATIONS am-kbn=2 AND am-lbn=1

丢番图方程α~m-kb=2和α~m-lb=1,其中k,l是给定的正整数,m>1,n>1,2×mn,包含了群论和组合论中一些未解决的问题。对于以上方程,本文用关于Pell方程的St(?)rmer定理,给出若干定理和推论。

The Diophantine equationswhere k be a given odd number, andwhere I be a given integer, containing some unsolved equations on group theory and combinato rial theory.For Diophantine equations (1) and(2) , we prove the following theorem.1. If equati n (1) has a positive integral solution such that then is the fundamental solution of2. If equation (2) has a positive integral solution such that , is the fundamental solution of