Re: representing polynomial range values as sums of 2 squares
- From: jankrihau@xxxxxxxxxxx
- Date: Sat, 21 Jul 2007 06:05:08 -0700
On 21 Jul, 14:55, quasi <qu...@xxxxxxxx> wrote:
A few more polynomial range conjectures ...
Let f be a polynomial in n variables, n>=1, with integer coefficients.
Regard f as a function from Z^n to Z.
Conjecture 1:
If f is nonconstant, then range(f) contains infinitely many elements
which can be represented as the sum of 2 squares of integers.
Wouldn't f(x) = 4x - 1 be a counterexample?
Conjecture 2:
If every element of range(f) is a sum of 2 squares of integers, then f
is a sum of 2 squares of polynomials with integer coefficients.
---
J K Haugland
http://home.no.net/zamunda
.
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