Integer Solutions Of Equations On A Class Of Uncertain Discussion And Research

The indeterminate equation (equations) is the oldest branch of number theory.It not only develops actively itself, but also is applied to every field of discrete mathematics. It plays an important role in our study, research, and solving the actual problems. So, many researchers have studied the indeterminate equation (equations) extensively and deeply in the domestic and abroad.Many authors have studied this kind of indeterminate equationsParticularly, they focused on some special forms of this kind of indeterminate equations, especially onδ₁,δ₂∈{±1,±2,±4}.However, because of the difficulty of solving such indeterminate equations, there is a vast study space on this problem.In this dissertation, some special forms of the above-mentioned indeterminate equations were studied by using elementary methods. The main achievements contained in this paper are as follows:1.All integer solutions of the indeterminate equationsare given.2.The integer solutions of the indeterminate equationsare discussed when D is an even square-free integer. 3. The integer solutions of the indeterminate equationsare discussed when D is the product of different odd primes.