ABSTRACT This nal project discusses the multiplicative functions commutable with sums of squares. In this nal project, suppose that k be an integer greater than or equal to 3. It is shown that if a multiplicative functions f satises f(x2 1 + x2 2 + · · · + x2 k) = f(x1)2 + f(x2)2 + · · · + f(xk)2 for all positive integers xi, then f is the identity function. This nal project i…