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Pell's Equation
* 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 andExpand
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Remarks on an Arithmetic Derivative
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-negativeExpand
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SEMI-ALGEBRAS THAT ARE LOWER SEMI-LATTICES
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
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Mathematical fallacies, flaws, and flimflam
1. Numbers 2. Algebra and trigonometry 3. Geometry 4. Finite mathematics 5. Probability 6. Calculus: limits and derivatives 7. Calculus: integration and differential equations 8. Calculus:Expand
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Euler Subdues a very Obstreperous Series
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Euler's 1760 paper on divergent series
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 academiaeExpand
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Algebra at the tertiary level
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 theExpand
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Three faces of proof
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Problems Leading to Pell’s Equation and Preliminary Investigations
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’sExpand
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