Syler 08.11.2010 23:08 Solve in equation: $ x^2+y^2+z^2+w^2=3(x+y+z+w) $ where $ x,y,z,w $ are positive integers.
mavropnevma 08.11.2010 23:31 This is a particular Hurwitz equation (see for example [R.K. Guy - Unsolved Problems in Number Theory]). Since (the coefficient) $3 < 4$ (the number of variables), Guy states that there is a finite set of solutions, which generate all others.