covering all N with squares (2nd degree polynomials with integer coeffs.).

[Brendan McKay]

* Simon Plouffe <simon.plouffe at sympatico.ca> [050127 22:57]:
> 
>  yes it does work but each new row is not
> of degree 2, (at least I don't think it is),

I still don't get it.  f(n) = n^2 + k is a polynomial of
degree 2 for each k.

> let my try to restate the problem
> 
> let's make a square array of numbers from wich
> each row is a 2nd degree pol. : apart from the
> first column, does the array covers ALL natural
> numbers with possibly some overlap?
 
I think you didn't say "apart from the first column" before, but it
makes little difference. Just use k+(n-1)^2 for n >= 0 and enough
values of k. If you allow only increasing rows, there is a problem
about including 1 but you can get everything else with k+n^2 for
n >= 0 and enough k's.

There is a problem about which 2-variable polynomials f(i,j)
cover the natural numbers for i,j>=0.  I think it is well
studied but I don't have references.

Brendan.