设这四个连续整数依次为:n-1,n,n+1,n+2,则
(n-1)n(n+1)(n+2)+1,
=[(n-1)(n+2)][n(n+1)]+1
=(n2+n-2)(n2+n)+1
=(n2+n)2-2(n2+n)+1
=(n2+n-1)2.
故四个连续整数的积加上1是一个整数的平方.
猜你喜欢
- 19分之4÷(3-7分之5*15分之14) 2分之1+(3分之1÷5分之2-3分之1) 7分之5*11分之7+11分之7*7分之6
- 2把一张长8厘米宽5分米的白纸围成一个圆柱形纸筒这个纸筒的体积是多少
- 3如右下图,定圆的半径为a,圆心为(b,c),则直线ax+by+c=0与直线 x-y+1=0的交点在第_象限.
- 4someone offers you a glass of wine.what do you say to refuse the offer
- 5He said he had bought a dictionary ()last week, and the dictionary was a great help to him
- 6英汉互译 超市____________(英语)
- 7已知水的比热容为4.2*10的3次方,1千克20摄氏度的水吸收了2.1*10的5次方焦的能量后温度升高到多少摄氏度?
- 835.25平方米等于几米乘与几米
- 9抒发了作者( )周总理的思想感情
- 10定义*是对有理数a,b进行的一种新运算,a*b=2ab+2008,试计算2*3*4的值