My favorite theorem - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Etc (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=4) +--- Forum: Community (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=6) +--- Thread: My favorite theorem (/showthread.php?tid=1022) My favorite theorem - tommy1729 - 08/15/2015 After my favorite sequence - the post about the binary partitions function - , Its time for my favorite theorem. --- One of my all-time leading candidates for Most Preposterous Theorem Ever: Definition: A polynomial f(x)∈C[x] is indecomposable if whenever f(x)=g(h(x)) for polynomials g, h, one of g or h is linear. Theorem. Let f,g, be nonconstant indecomposable polynomials over C. Suppose that f(x)−g(y) factors in C[x,y]. Then either g(x)=f(ax+b) for some a,b∈C, or degf=degg=7,11,13,15,21, or 31, and each of these possibilities does occur. --- Copied from here Grahams post http://mathoverflow.net/questions/14076/irreducibility-of-polynomials-in-two-variables I was aware of it since a very long time , but despite " old " this is Nice !! Regards Tommy1729