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Article #65Re: Inequalities for Fermat's last theorem
From: hporopudas
Date: Wed, 04 Nov 1992 08:44
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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Newsgroups: sci.logic Path: arc1-ca.pugleaf.net!sparky!uunet!europa.asd.contel.com!paladin.american.edu!news.univie.ac.at!hp4at!mcsun!news.funet.fi!funic!nokia.fi!tnclus.tele.nokia.fi!hporopudas From: hporopudas@tnclus.tele.nokia.fi Subject: Re: Inequalities for Fermat's last theorem Message-ID: <1992Nov4.104403.1@tnclus.tele.nokia.fi> Lines: 53 Sender: usenet@noknic.nokia.fi (USENET at noknic) Nntp-Posting-Host: tne02.tele.nokia.fi Organization: Nokia Telecommunications. References: <1992Oct29.093106.1@tnclus.tele.nokia.fi> <1992Nov2.090701.1@tnclus.tele.nokia.fi> <1992Nov3.123313.1@tnclus.tele.nokia.fi> Date: Wed, 4 Nov 1992 08:44:03 GMT