Repunits #67 of Gottschalk’s Gestalts A Series Illustrating Innovative Forms of the Organization & Exposition of Mathematics

Source URL: gottschalksgestalts.org

• Number theory
• Integer sequences
• Repunit
• Probable prime
• Prime number
• Mersenne prime
• Coprime
• 11
• 17
• Numbers
• Mathematics
• Integers

ON LINEAR COMBINATIONS OF UNITS WITH BOUNDED COEFFICIENTS AND DOUBLE-BASE DIGIT EXPANSIONS ¨ DANIEL KRENN, JORG THUSWALDNER, AND VOLKER ZIEGLER

Source URL: finanz.math.tu-graz.ac.at

• Algebraic number theory
• Field theory
• Algebraic integer
• Integers
• Algebraic number field
• Diophantine approximation
• Discriminant of an algebraic number field
• Auxiliary function
• Mathematics
• Abstract algebra
• Mathematical analysis

On quantitative aspects of the unit sum number problem Clemens Fuchs, Robert Tichy and Volker Ziegler Abstract. We investigate the function uK,S (n; q) which counts the number of representations of algebraic integers α

Source URL: finanz.math.tu-graz.ac.at

• Number theory
• Mathematics
• Modular arithmetic
• Quadratic residue

THE NUMBER OF PRIME DIVISORS OF A PRODUCT OF CONSECUTIVE INTEGERS R. BALASUBRAMANIAN, SHANTA LAISHRAM, T. N. SHOREY, AND R. THANGADURAI Abstract. It is shown under Schinzel’s Hypothesis that for a given ` ≥ 1, there

Source URL: www.math.tifr.res.in

• Number theory
• Coprime
• Chinese remainder theorem
• Prime number
• Arithmetic function
• Euclidean algorithm
• Mathematics
• Modular arithmetic
• Abstract algebra

IRREDUCIBILITY OF GENERALIZED HERMITE-LAGUERRE POLYNOMIALS SHANTA LAISHRAM AND T. N. SHOREY 1. Introduction Let n and 1 ≤ α < d be positive integers with gcd(α, d) = 1. Any positive rational

Source URL: www.math.tifr.res.in

• Mathematics
• Laguerre polynomials
• Commutative algebra
• Modular arithmetic
• Number theory
• Mathematical analysis
• Abstract algebra
• Polynomials

Theorems of Sylvester and Schur T.N. Shorey An old theorem of Sylvester states that a product of k consecutive positive integers each exceeding k is divisible by a prime greater than k. We shall

Source URL: www.math.tifr.res.in

• Algebraic number theory
• Newton polygon
• Commutative algebra
• Localization
• Measure theory
• Valuation ring
• Radon–Nikodym theorem
• Abstract algebra
• Algebra
• Mathematics

Generalizations of some irreducibility results by Schur T.N. Shorey and R. Tijdeman October 16, 2009 Section 1. Introduction Let a ≥ 0 and a0 , a1 , . . . , an be integers with

Source URL: www.math.tifr.res.in

• Polynomials
• Algebra
• Inverse Galois problem
• Laguerre polynomials
• Irreducible polynomial
• Binomial coefficient
• Factorization of polynomials over a finite field and irreducibility tests
• Mathematics
• Mathematical analysis
• Abstract algebra

THE EQUATION n(n + d) · · · (n + (k − 1)d) = by 2 WITH ω(d) ≤ 6 OR d ≤ 1010 SHANTA LAISHRAM AND T. N. SHOREY Abstract. For relatively prime positive integers n and d, a well-known Conjecture states that n(n + d

Source URL: www.math.tifr.res.in

Solving Solvingproblems problems Geometry Geometry

Source URL: www.cobbk12.org

• Numbers
• Figurate numbers
• Integer sequences
• Cube
• Integers
• Number theory
• Number
• Directly Observed Therapy – Short Course
• Addition
• Mathematics
• Abstract algebra
• Elementary arithmetic

Do the Integers Exist? The Unknowability of Arithmetic Consistency JACK T. SCHWARTZ Courant Institute It is an article of faith for most mathematicians that Peano’s axioms for arithmetic are consistent, perhaps becaus

Source URL: www.multimedialibrary.com

• Axiom
• Mathematical proof
• Foundations of mathematics
• Peano axioms
• Kurt Gödel
• Contradiction
• Zermelo–Fraenkel set theory
• Theorem
• Gottlob Frege
• Logic
• Mathematics
• Mathematical logic