Arranging the Solutions of f(x+y+z) = xyz
Image via Wikipedia Arranging the Solutions of f(x+y+z) = xyz Arranging the Solutions of f(x+y+z) = xyz For any quadratic polynomial f(s) = as 2 + bs + c with integer coefficients a,b,c, consider the Diophantine equation f(x+y+z) = xyz. In other words, for fixed integers a,b,c we have the equation If there exists a solution x,y,z to this equation, then z is a root of the quadratic This can also be written in the form Interestingly, we have z 2 = f(x+y)/a for a solution (x,y,z) if and only if (x,y) is a solution of f '(x+y) = xy. Related articles Graphing Equations (trigandstuff.wordpress.com) Game Changing Conjectures In Mathematics (rjlipton.wordpress.com) Pre Calculus:::: (trigandstuff.wordpress.com) The del Ferro-Tartaglia-Cardano solution of the cubic (talkmath.wordpress.com) Large values of the Gowers-Host-Kra seminorms (terrytao.wordpress.com) Quadratic Residues - I (mathematicaldreams.wordpress.com) Monday Math: Infinite Descent ...