منابع مشابه
Problems in Elementary Number Theory
Introduction The heart of Mathematics is its problems. Paul Halmos Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting problems in elementary Number Theory. Many of the problems are mathematical competition problems from all over the world like IMO, APMO, APMC, Putnam and many others. The book has a supporting website at which h...
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I would like to illustrate the problems which I shall investigate in this paper by an example. Denote by r&z) the maximum number of integers not exceeding n, no k of which form an arithmetic progression. The problem is to determine or estimate the value of rk(n). This problem is connected with several known questions of number theory. If r&) <(I-t)n/log n for every K, if n is sufficiently large...
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A k = max(p,+ t p,), k < p, < p, + , < 2k . In fact I cannot even disprove f(k) = Ak for all sufficiently large k, though it seems likely that f(k) > Ak for all large k. A well known theorem of Pólya and Störmer states that if u > uo(k) then u(u + 1) always contains a prime factor greater than k, thusf(k) can be determined in a finite number of steps, and an explicit bound has been given by Leh...
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The essay can be divided in two parts, each dedicated to each of the problems mentioned above. I begin by introducing inquisitive semantics, doing so by inserting it on what I dub ‘Weak Dynamic Approaches’ to meaning, focusing on what is specific on the inquisitive approach. The notions of informative and inquisitive content will be introduced, as the recursive definition of a proposition. I pr...
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In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not divisible by any large prime factors. The first is the Ramsey-theoretic problem to determine the maximal size of a subset of the integers containing no 3...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1978
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093888210