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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1828.0. "Crux Mathematicorum 1892" by RUSURE::EDP (Always mount a scratch monkey.) Wed Dec 29 1993 11:03

    Proposed by Marcin E. Kuczma, Warszawa, Poland.
    
    Let n >= 4 be an integer.  Find the exact upper and lower bounds for
    the cyclic sum
    
         n           x[i]
    	sum ----------------------
        i=1 x[i-1] + x[i] + x[i+1]
    
    (where of course x[0] = x[n], x[n+1] = x[1]), over all n-tuples of
    nonnegative numbers (x[1], ..., x[n]) without three zeros in cyclic
    succession.  Characterize all cases in which either one of these bounds
    is attained.
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