This paper is concerned with finite sequences of integers that may be written as sums of squares of two nonzero integers. We first find infinitely many integers $n$ such that $n,n+h$ and $n+k$ are all sums of two squares where $h$ and $k$ are two arbitrary integers, and as an immediate corollary obtain, in parametric terms, three consecutive integers that are sums of two squares. Similarly we obtain $n$ in parametric terms such that all the four integers $n,n+1,n+2,n+4$ are sums of two squares. We also find infinitely many integers $n$ such that all the five integers $n,n+1,n+2,n+4,n+5$ are sums of two squares, and finally, we find infinitely many arithmetic progressions, with common difference $4$, of five integers all of which are sums of two squares.

本文关注的是可以写成两个非零整数的平方和的有限整数序列。我们首先找到无穷多个整数$n$这样$n,n+H$和$n+k$都是两个平方和，其中$H$和$k$是两个任意整数，并且作为直接推论，以参数术语形式获得三个连续整数，它们是两个平方和。同样我们得到$n$用参数术语来说，所有四个整数$n,n+1,n+2,n+4$是两个平方和。我们还发现无穷多个整数$n$使得所有五个整数$n,n+1,n+2,n+4,n+5$是两个平方和，最后，我们发现无穷多个具有公差的算术级数$4$，五个整数，它们都是两个平方和。