The peculiar (monic) polynomials, the zeros of which equal their coefficients
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- 10.1080/14029251.2017.1375690How to use a DOI?
- zeros of polynomials; Ulam polynomials
We evaluate the number of complex monic polynomials, of arbitrary degree N, the zeros of which are equal to their coefficients. In the following, we call polynomials with this property peculiar polynomials. We further show that the problem of determining the peculiar polynomials of degree N simplifies when any of the coefficients is either 0 or 1. We proceed to estimate the numbers of peculiar polynomials of degree N having one coefficient zero, or one coefficient equal to one, or neither.
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
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Cite this article
TY - JOUR AU - F. Calogero AU - F. Leyvraz PY - 2021 DA - 2021/01/06 TI - The peculiar (monic) polynomials, the zeros of which equal their coefficients JO - Journal of Nonlinear Mathematical Physics SP - 545 EP - 555 VL - 24 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1375690 DO - 10.1080/14029251.2017.1375690 ID - Calogero2021 ER -