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From: kenner@cmcl2.UUCP
Newsgroups: net.math
Subject: Re: Re: Simple Problem?? - (nf)
Message-ID: <34158@cmcl2.UUCP>
Date: Sat, 22-Oct-83 17:32:28 EDT
Article-I.D.: cmcl2.34158
Posted: Sat Oct 22 17:32:28 1983
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#R:lanl-a:-299100:cmcl2:27800002:000:849
cmcl2!kenner    Oct 22 17:32:00 1983

Maybe a present-day high-schooler can't do it in 10-15 minutes but a real
old-timer should be able to do it in far less time.

See sections 562 and 563 (pages 468-9) in Hall and Knight for the method.
Put simply, the sum of the nth powers of the roots of f(x)=0 is the
coefficient of x**(-n) in f'(x)/f(x).  If I haven't made a mistake, the sum
of the 17th powers is 17 (the sum of the 15th powers is -45, the 16th is
-32, the 30th is -135 (I haven't computed the ones higher, the lower ones
that I haven't given are all zero)).

Hall and Knight is a very interesting book in which to find things of this
sort.  For those not familiar with it, it was first published in 1887.  The
edition I have was from 1957.  It's title is "Higher Algebra: A sequel to
Elementary Algebra for Schools" and it is published by Macmillan & Co. and
St. Martins Press.