Multiplicative structure of integers, shifted primes and arithmetic functions Kevin Ford http://www.math.uiuc.edu/∼ford/erdos100.pdf University of Illinois at Urbana-Champaign

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A PRELUDE TO THE STUDY OF RECIPROCITY LAWS JONAH SINICK 1. A case of quadratic reciprocity Consider the set of integers that are 5 less than a square number, that is, numbers of the form P (n) = n2 − 5 for n = 1, 2, 3,

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19th Nordic Mathematical Contest April 5, 2005 Problem 1. Find all positive integers k such that the product of the digits of k, in the decimal system, equals

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FactInt Advanced Methods for Factoring Integers VersionJune 16, 2011

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Is it better to be born Rich or Lucky? The mathematics of random walks. The set-up. Let a and ` be integers, with 1 ≤ a ≤ 7 and 2 ≤ ` ≤ 5.

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Integers with a divisor in a given interval Kevin Ford MarchDefine τ (n, y, z) = |{d|n : y < d ≤ z}|.

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COMPUTER SCIENCE TRIPOS Part IB – 2012 – Paper 5 2 Computer Design (SWM) Consider the following code which takes an array d of n 32-bit integers and performs a bubble sort.

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TRANSFINITE APPROXIMATION OF HINDMAN’S THEOREM ¨ MATHIAS BEIGLBOCK AND HENRY TOWSNER A BSTRACT. Hindman’s Theorem states that in any finite coloring of the integers, there is

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• Height
• Infinite group theory
• Ordinal number
• Spectral theory
• Operator theory
• Representation theory
• Symbol
• Orbifold
• Abstract algebra
• Mathematics
• Group theory

Aya Karpinska and Daniel C

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• Elementary arithmetic
• Integers
• Number theory
• Mathematics
• Numbers
• Cube

Math Competition: Review 1 Khamsi ProblemShow that every positive integer is a sum of one or more numbers of the form 2r 3s , where r and s are nonnegative integers and no summand divides another. (For example

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