Question

已知n为整数,试说明(n+5)^2-(n-1)^2的值一定能被12整除

如题~
谁帮我解答一下
^2的意思是平方

Answer 1

n^2+10n+25-n^2+2n-1
=12n+24
=12(n+1)

12(n+1)/12=n+1

因为n为整数，所以n+1为整数
所以能被12整除

Answer 2

(n+5)^2-(n-1)^2
=[(n+5)+(n-1)][(n+5)-(n-1)]
=(2n+4)*6
=12(n+2)
一定能被12整除

Answer 3

(n+5)^2-(n-1)^2=n^2+10n+25-n^2+2n-1=12n+24=12(n+2)
12(n+2)必然被12整除