Given any positive real number r there will exist some positive real numbers r1, r2,…,rn all less than 4 with

That surprising ‘simultaneous factorisation’ is established in this article. It is based on some fuller work which I did a couple of years ago, but the interest in it was revived when Nick Mackinnon’s and Nick Lord’s work on ‘Sums equal to products’ was published in the March 1986 Gazette.