Tetration Forum
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


I was aware of it since a very long time , but despite " old " this is Nice !!