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2^n-1 and square

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  • Lio David
    Puzzle:  find  the   next square number after 2^n- 1 solution  : (3*2^k)^2   note : k =  (n-3)/2                       example :
    Message 1 of 2 , Oct 4, 2009
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      Puzzle:  find  the   next square number after 2^n- 1


      solution  : (3*2^k)^2
       
      note : k =  (n-3)/2

                            example :
      n =  43112609

      2^n-1 <     (3*2^k)^2           
                <    (3*2^21556303)^2

      ----------------
      n = 7
      2^7-1 <   (3*2^2)^2
                 <  12^2                             we have    11^2 <  2^7-1 < 12^2

      Are there any other solutions

      rachid




      [Non-text portions of this message have been removed]
    • djbroadhurst
      ... That s rather easy when n is a positive even integer. Perhaps you might exercise some discipline and make clear the precise type of number n to which
      Message 2 of 2 , Oct 4, 2009
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        --- In primenumbers@yahoogroups.com,
        Lio David <maths_forall@...> wrote:

        > Puzzle: find the next square number after 2^n-1

        That's rather easy when n is a positive even integer.

        Perhaps you might exercise some discipline
        and make clear the precise type of number "n"
        to which your ill-defined "puzzle" refers?

        David
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