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From: gmf@uvacs.UUCP
Newsgroups: net.math
Subject: Pell equation (comment)
Message-ID: <1263@uvacs.UUCP>
Date: Sat, 28-Apr-84 05:03:38 EDT
Article-I.D.: uvacs.1263
Posted: Sat Apr 28 05:03:38 1984
Date-Received: Sun, 29-Apr-84 09:11:15 EDT
Lines: 14


As to the least positive solution for Pell equation for 991
(viz.,x = 30 digit number, y = 29 digit number):

Suppose someone formulates the theorem

     x^2 - 991*y^ = 1 has no positive solution.

If he/she tries to verify this by selecting y=1,2,... and showing
there is no corresponding x, success would occur for something
more than 10^28 trials.  This is a good example for showing
that non-mathematical induction is a perilous technique.

     Gordon Fisher