A note on a result of B. Bojan

Abstract. We determine all solutions of those functions \(f:{\mathbb N}\to {\mathbb C}\) for which \(f(n^2+m^2+k)= f^2( n)+f^2(m)+K\) is satisfied for all positive integers \(n,m\), where a
non-negative integer \(k\) and \(K\in{\mathbb C}\) are given. This improves the result of B. Bojan.