* The square root of 2 * Problems leading to Pell's equation and preliminary investigations * Quadratic surds * The fundamental solution * Tracking down the fundamental solution * Pell's equation and… Expand

Let D(n) denote a function of an integral variable n ≥ 0 such that (1) D(1) = D(0) = 0
(2) D(p) = 1 for every prime p
(3) D(n 1 n 2 ) = n 1 D(n 2 ) + n 2 D(n 1 ) for every pair of non-negative… Expand

This paper is concerned with uniformly closed sets ofcontinuous real-valued functions defined on a compactHausdorff space that are at the same time semi-algebras(wedges closed under multiplication)… Expand

That Euler was quite aware of the subtleties of assigning a sum to a divergent series is amply demonstrated in his paper De seriebus divergentibus which appeared in Novi commentarii academiae… Expand

Abstract Inevitably, in such discussion groups, the time is too short to handle topics to the depth that they deserve. It is hoped that these notes will provide some hint of the discussions in the… Expand

The first chapter presented a situation that led to pairs of integers (x, y) that satisfied equations of the form x 2 - 2y 2 = k for some constant k. One of the reasons for the popularity of Pell’s… Expand