Question

若a是自然数,求证:a(a+1)(a+2)(a+3)+1必为完全平方数

Answer 1

显然有:a(a+1)(a+2)(a+3)+1=(a^2+3a+2)(a^2+3a)+1

=(a^2+3a+1)(a^2+3a+1)=(a^2+3a+1)^2