令1996=x
原式=x(x+1)(x+2)(x+3) +1
=[x(x+3)][(x+1)(x+2)] +1
=(x^2+3x)(x^2+3x+2) +1
=(x^2+3x)^2+ 2*（x^2+3x)+1
=(x^2+3x+1)^2
所以1996×1997×1998×1999＋1是一个完全平方数