2000 Putnam A2

Prove that there exist infinitely many integers $n$ such that

$n,n+1,n+2$ are each the sum of the squares of two integers.

[Example: $0=0^2+0^2$, $1=0^2+1^2$, $2=1^2+1^2$.]

证明存在无限多个整数 $n$ 使得

$n,n+1,n+2$ 分别是两个整数的平方和。

[示例：$0=0^2+0^2$、$1=0^2+1^2$、$2=1^2+1^2$。]