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20214Lehmer sequence puzzle

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  • Mike Oakes
    May 7, 2009
      For integer R>=1, Q>=1, and odd n>=1, define the Lehmer sequence
      LV(R,Q,n) = (x^n+y^n)/(x+y)
      where x = sqrt(R)/2+sqrt(R-4*Q)/2
      and y=sqrt(R)/2-sqrt(R-4*Q)/2

      For given R,Q, define u(R,Q) to be the number of values of n for which LV() is a unit (i.e. +/-1).

      Puzzle: what is max{R>=1,Q>=1}(u(R,Q))?

      -Mike Oakes, per proxy SPQR,
      Society for Preservation of sQuare Roots
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