关于一类整值多项式平方数的研究

Research on the square integers of a kind of integral valued polynomial

运用Pell方程的性质讨论了形如f(n,x)的平方数,其中f(n,x)=1+(1/2)n2 x(x+1),n,x∈N+.证明了对于任意给定的正整数n存在无穷多个正整数x可使f(n,x)是平方数.

In this paper, using the properties of Pell equation, the square integers of the form f（n,x）= 1 q-（1/2）n2x（x-q-1） are discussed, where n and x are all positive integers. It is proved that infinite positive integers x are existed which make f（n,z） are square integers for any fixed n.