RE: [math-fun] Re: covering all N with squares (2nd degree polynomialswith integer coeffs.).
1. Are there any restrictions on the cocefficients, or can they be arbitrary complex numbers? 2. As long as each natural number occurs somewhere in the array, does it matter what else is in the array? --Dan ------------------------------------------------------ Simon says: << ... 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?
No, rule 1, only polynomials with integer coeffs. rule 2, there can be some overlap. rule 3, avoid the first trivial column. rule 4, only N, not Z. I wanted to explicitely write down a set of polynomials with the desired results, as we know pol. of degree 2 are sparse compared to all integers, I was wondering if it was plain impossible or trivially possible. Simon Plouffe
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Daniel Asimov -
Simon Plouffe