Question

Prove that N= 996x997x998x999+1 is perfect squat.

Answer 1

\[N=m(m+1)(m+2)(m+3)+1=(m^2+3m)(m^2+3m+2)+1=\]\[=(m^2+3m+1-1)(m^2+3m+1+1)+1=\]\[=(m^2+3m+1)^2-1+1=(m^2+3m+1)^2\]