[tex]\displaystyle \\
n^2+n+41 = n(n+1) + 41 \\
n+1 = 41 \\
\Longrightarrow ~~~ n(n+1) + 41 = n \times 41 +41 = 41(n+1) = 41 \times 41=pp\\
\Longrightarrow ~~~ n = 41-1 = \boxed{40} \\ \\
Verificare: \\
n^2+n+41 = 40^2 + 40 + 41 =1600 + 40+41 = 1681 = 41^2 = pp[/tex]
[tex] sau \\
n^2+n+41 = 40^2 + 40 + 41 = 40(40+1) + 41 = \\
= 40 \times 41 + 41 = 41(40 +1) = 41 \times 41 = 41^2 = pp[/tex]
