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From: moews@husc2.UUCP (moews)
Newsgroups: net.puzzle,sci.math
Subject: Re: Algebra (spoiler)
Message-ID: <1029@husc2.UUCP>
Date: Sat, 15-Nov-86 20:56:02 EST
Article-I.D.: husc2.1029
Posted: Sat Nov 15 20:56:02 1986
Date-Received: Sun, 16-Nov-86 01:45:17 EST
References: <660@hoxna.UUCP>
Reply-To: moews@husc4.UUCP (David Moews)
Organization: Harvard University Science Center
Lines: 27
Xref: mnetor net.puzzle:1581 sci.math:199

In article <660@hoxna.UUCP> tom@hoxna.UUCP ( Tom McGuigan ) writes:
>>A + B + C = 1, A^2 + B^2 + C^2 = 2, A^3 + B^3 + C^3 = 3
>
>(omitting pages and pages of algebraic manipulation)
>
>==> A^4 + B^4 + C^4 = 4.5
>
>Tom McGuigan
>..!ihnp4!homxb!hoxna!tom
   
    This puzzle is more interesting if you let 3=n (i.e., if
a[1]+...+a[n] = 1, a[1]^2 + ... + a[n]^2 = 2, ..., a[1]^n + ... + a[n]^n = n,
what is a[1]^(n+1) + ... + a[n]^(n+1)?)   In this case, the answer can be
shown to be the coefficient of x^n in 


      1 - 1/(1-x)                                  
    e             - 1            2         3 
  - ----------------- = x + 5/2 x  + 25/6 x  + ...,
            2
       (1-x)  

(use Newton's identities),

so the answer is 25/6 (not 9/2; check your algebra.)
--
David Moews     moews@husc4.harvard.edu     ...!harvard!husc4!moews