From: John Robertson <jpr2718@aol.com>
Subject: Size of Fundamental Solution to Pell Equation
Date: Sun, 24 Dec 2000 20:23:09 GMT
Newsgroups: sci.math
Summary: [missing]

Let t, u be the least positive solution to x^2 - dy^2 = 4.  Let e=(t +
u*sqrt(d))/2.  Schur, Gottingen Nachrichter, 1918, pp. 30-36, shows e <
d^d^(1/2).  Loo-Keng Hua, Bulletin of the AMS, vol 48, 1942, p 731,
shows for d == 0 or 1 (mod 4) that log e < (d^(1/2))*((1/2) log d + 1).

Has this bound been improved?  Is it the best possible?

I am just curious.  Any references would be appreciated.  Please reply
to sci.math, or to my email address, or both.

John Robertson

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==============================================================================

From: Jpr2718@aol.com (John P. Robertson)
Subject: Least Positive Solution to Pell Equation
Date: 8 Jan 01 17:30:19 GMT
Newsgroups: sci.math.numberthy

Let t, u be the least positive solution to x^2 - dy^2 = 4.  Let e=(t +
u*sqrt(d))/2.

Schur, Gottingen Nachrichter, 1918, pp. 30-36, shows e < d^d^(1/2).  Loo-Keng
Hua, Bulletin of the AMS, vol 48, 1942, p 731, shows for d == 0 or 1 (mod 4)
that log e < (d^(1/2))*((1/2) log d + 1).

Have these bounds been improved?  Are they the best possible?

John Robertson
JPR2718@AOL.COM