题目不对,是a=2001²+2001²×2002²+2002² 吧?
令A = 2001,A + 1 = 2002
a=2001²+2001²×2002²+2002²
= A² + A² * (A + 1)² + (A + 1)²
= [A(A + 1)]² + 2A² + 2A + 1
= [A(A + 1)]² + 2A(A + 1) + 1
= [A(A + 1)]² + 2[A(A + 1)]*1 + 1²
= [A(A + 1) + 1]²
也就是
= [2001*(2001+1) + 1]²
= 4006003²