SQUARE FREE VALUES OF THE ORDER FUNCTION FRANCESCO PAPPALARDI Abstract. Given a ∈ Z \ {±1, 0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This

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The riddle The conjecture Consequences

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• Mathematics
• Conjectures
• Number theory
• Discrete mathematics
• Abc conjecture
• Prime number
• Coprime integers
• MasonStothers theorem
• Radical of an integer

Number theory 1. k1 , k2 , r, s ∈ N , k1 ≤ 2k2 . Suppose that k1 |rs . Show that k1 |rk2 P roof1 : ( We have

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• Number theory
• Coprime integers

How Euler Did It by Ed Sandifer Odd Perfect Numbers November 2006 The subject we now call “number theory” was not a very popular one in the 18th century. Euler wrote almost a hundred papers on the subject, but the fi

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• Integer sequences
• Number theory
• Divisor function
• Algebraic number theory
• Perfect number
• Modular arithmetic
• Amicable numbers
• Divisor
• Prime number
• Quadratic reciprocity
• Leonhard Euler
• Coprime integers

Visibility in Random Forests Abigail Turner, Ananya Uppal, Peng Xu, Amita Malik (Graduate Student), Prof. Jayadev Athreya, Prof. Francesco Cellarosi (Faculty Mentors) Overview

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• Probability distributions
• Number theory
• Infinitely divisible probability distributions
• Probability theory
• Poisson processes
• Farey sequence
• Coprime integers
• Normal distribution
• Central limit theorem
• Random variable
• Exponential distribution

On Cornacchia’s algorithm for solving the diophantine equation u2 + dv 2 = m F. Morain ∗† J.-L. Nicolas ‡ September 12, 1990

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• QN
• Euclidean algorithm
• Diophantine approximation
• Coprime integers
• Diophantine equation

471 Old Idaho Usual Here Robert Israel, Stephen Morris, and Stan Wagon N. Kildonan [1℄ raised the following problem. Take an arbitrary word

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• Elementary number theory
• Number theory
• Integer sequences
• Divisibility rule
• Division
• Coprime integers
• Singly and doubly even

183 Documenta Math. Families of p-Divisible Groups with Constant Newton Polygon

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• Algebraic groups
• Number theory
• Algebraic number theory
• Divisible group
• Witt vector
• Morphism of schemes
• BarsottiTate group
• Group scheme
• Coprime integers
• Ramification
• Distribution
• Morphism of algebraic varieties

Explicit Primality Criteria for h #2k ± 1 Wieb Bosma Mathematics of Computation, Vol. 61, No. 203, Special Issue Dedicated to Derrick Henry Lehmer. (Jul., 1993), ppStable URL: http://links.jstor.org/sici?sici=

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• Mathematics
• Discrete mathematics
• Number theory
• Modular arithmetic
• Integer sequences
• Finite fields
• Quadratic residue
• Prime number
• Quadratic reciprocity
• XTR
• Coprime integers
• Factorial

Math Wrangle Practice Problems American Mathematics Competitions December 22, !)!)! , = k . n!, where k and n are positive integers and n

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• Algebraic number theory
• Integer sequences
• Elementary number theory
• Integer
• Ring theory
• Prime number
• Coprime
• Number
• Floor and ceiling functions
• Mathematics
• Abstract algebra
• Number theory