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Article #65

Re: Inequalities for Fermat's last theorem

#65
From: hporopudas
Date: Wed, 04 Nov 1992 08:44
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In article <1992Nov3.123313.1@tnclus.tele.nokia.fi>,
hporopudas@tnclus.tele.nokia.fi writes:

..all deleted from above message...

So we have:

  Following inequality holds:

              n   n      n    2
             y - x  <  (x  -1)  - 1

  From which we have the inequality:

                   2
             z <  x



  K. Inkeri's result:
  ------------------
                          3n-4
             x  >  (1/2) n     ; for n is prime exponet > 2

      (0 < x < y < z, x,y,z are relatively-prime integers)
      (It can also be assumed without loss of generality that
       x and y are relatively prime to p).

      Two cases of Fermat's last theorem:
      ----------------------------------
                                            3
                                          2n + n   n
      If (xyz,n)=1, (Case I), then x > ( -------- )  , n is prime exponent > 2.
                                         log(3n)

      (Case II is when n divides z, n is prime exponent > 2).


    Reference:

    Inkeri, K, 1953.
    Absch{tzungen fur eventuelle L|sungen der Gleichung
    im Fermatschen Problem.
    Ann. Univ. Turku, Ser. A, vol. 16, no. 1, pages 3-9.


    I remove this discussion to sci.math.research, because I received
    here in sci.logic none valuable comments.


 ---Hannu.
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From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Inequalities for Fermat's last theorem
Message-ID: <1992Nov4.104403.1@tnclus.tele.nokia.fi>
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Date: Wed, 4 Nov 1992 08:44:03 GMT