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From: mbmonagan@watmum.UUCP (Michael B. Monagan)
Newsgroups: sci.math.symbolic
Subject: help needed to factor an integer
Message-ID: <664@watmum.UUCP>
Date: Thu, 6-Nov-86 00:26:16 EST
Article-I.D.: watmum.664
Posted: Thu Nov  6 00:26:16 1986
Date-Received: Thu, 6-Nov-86 21:41:12 EST
Distribution: net
Organization: U of Waterloo, Ontario
Lines: 18

Andrew Granville and I have been working on the First case of
Fermat's Last Theorm.  Specifically, we are attempting to show that

		 p    p    p
		x  + y  = z

there does not exist positive integers x,y and z and a p prime less than
4*10^15 which does not divide x y z, which satisfy the above equation.
Part of the proof involves showing that for each prime p dividing
integers g[n], p^2 does not divide 2^p - 2.  Thus the integers g[n]
require factorization.  Several of the g[n] are well over 100 digits
in length.  We have been successful in factoring all but one of these
integers using a number of algorithms, including Lenstra's elliptic
curve algorithm.  However, we are stuck on the 68 digit number below

g[34] := 45342330653448983777029327888871061430657597465656786489926540403841;

We would very much appreciate any help with factoring this integer.