English

Polynomials involving the floor function

Number Theory 2008-02-03 v1

Abstract

Some identities are presented that generalize the formula x^3 = 3x floor(x floor(x)) - 3 floor(x) floor(x floor(x)) + floor(x)^3 + 3 frac(x) frac(x floor(x)) + frac(x)^3 to a representation of the product x_0x_1 ... x_{n-1}.

Keywords

Cite

@article{arxiv.math/9504229,
  title  = {Polynomials involving the floor function},
  author = {Inger Johanne Håland and Donald E. Knuth},
  journal= {arXiv preprint arXiv:math/9504229},
  year   = {2008}
}