Question

设a=2008×2010×2012×2014+16,请你证明a是一个完全平方数。

Answer 1

a=2008×2010×2012×2014+16,
=2008×[2008+2][2014-2]2014+16
=[2008²+2×2008][2014²-2×2014]+16
=2008²×2014²-2×2008^2×2014+2×2008×2014²-4×2008×2014+16
=2008²×2014²-2×2008×2014×[2008-2014+2]+16
=2008²×2014²+8×2008×2014+16
=[2008×2014+4]²
所以，a是一个完全平方数。

Answer 2

(2011 - 3) * (2011 + 3) * (2011 - 1) * (2011 + 1)
= (2011^2 - 9) * (2011^2 - 1) + 16
= (2011^2)^2 - 10* (2011^2) + 9 + 16
= （2011^2 - 5）^2