Question

2×4×6×8+16=400 4×6×8×10+16=1936 6×8×10×12+16=5776 …… 有什么规律?请

Answer 1

结论是相邻四个偶数的乘积加上16,必然是一个整数的平分.

设这四个偶数分别是：2n、2(n+1)、2(n+2)、2(n+3)

则：

2n*2(n+1)*2(n+2)*2(n+3)+16

=16*[n(n+1)(n+2)(n+3)+1]

=16*{[n(n+3)]*[(n+1)(n+2)]+1}

=16 {n(n+3)[n(n+3)+2]+1}

=16[n(n+3)^2 + 2n(n+3)+1]

=16[n(n+3)+1]^2

= [2n*2(n+3)+4]^2

= [4n(n+3)+4]^2