À propos de l’équation fonctionnelle
\(f(m^2 + Dmn + n^2) = f(m)^2 + Df(m)f(n) + f(n)^2\)

Abstract. When \(D\in\{4,\, 5,\, 6\}\), we prove that the only solution to the functional equation \(f(m^2+Dmn+n^2)=f(m)^2+Df(m)f(n)+f(n)^2\) with \(f(1)=1\) is the identity function.