Maybe someone already mentioned this, but this problem is a simplified formulation of a famous number thoery riddle called 'The Sum and Product Riddle' which is

Maybe someone already mentioned this, but this problem is a simplified formulation of a famous number thoery riddle called 'The Sum and Product Riddle' which is even more baffling. Here it is http://blog.computationalcomplexity.org/2007/01/sum-and-product-riddle.html?m=1 http://blog.computationalcomplexity.org/2007/01/sum-and-prod...