Arnold's "strange infinite sequence of degrees"
N. J. A. Sloane
njas at research.att.com
Tue Feb 22 16:28:11 CET 2005
To Math-Fun, Seq-Fans:
There is an article by Arnold which has appeared in several places.
There are two versions in English:
MR2080045 Arnold, V. I. From Hilbert's superposition problem to dynamical systems [ MR1733564 (2001h:01031)]. Amer. Math. Monthly 111 (2004), no. 7, 608--624. 01A65 (01A60 37-03 54H20)
MR1733564 (2001h:01031) Arnold, V. I. From Hilbert's superposition problem to dynamical systems. The Arnoldfest (Toronto, ON, 1997), 1--18, Fields Inst. Commun., 24, Amer. Math. Soc., Providence, RI, 1999. (Reviewer: Stanis\l aw Janeczko) 01A65 (01A60 37-03 54H20)
Footnote 2 says:
"Starting from degree 9, one can kill one more coefficient. The
known possibilities to kill more coefficients occur along a rather
strange infinite sequence of degrees."
He is refering to the problem of putting a polynomial equation
f(X)=0 into canonical form. E.g. any 5th degree equation can be
reduced to x^5 + aX + 1 = 0.
My question is, what is this "strange infinite sequence of degrees"?
Thanks
Neil Sloane
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