# elementary number theory question

One easy way to do this is to use Lagrange multipliers, optimizing $f(x_1,x_2,\ldots,x_n)=x_1+x_2+\ldots+x_n$ subject to the constraint $g(x_1,x_2,\ldots,x_n)=x_1 x_2\cdots x_n=1$.