(n^2-n-1)(n^2-n+1)+1 este patrat perfect?
Notam: n^2-n-1=t
Atunci n^2-n+1=(n^2-n-1)+2=t+2
Si avem:
t(t+2)+1=t^2+2t+1=(t+1)^2
Revenind la notatia initiala:
(n^2-n-1)(n^2-n+1)+1=( n^2-n-1+1)^2=(n^2-n)^2 care e patrat perfect.
