08/15/2015, 09:58 PM

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/...-variables

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

Regards

Tommy1729

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/...-variables

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

Regards

Tommy1729