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+--- 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.
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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.
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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