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Primes modulo which almost all Fermat numbers are primitive roots
A prime is called elite, or anti-elite, when all but finitely many    Fermat numbers are quadratic nonresidues or residues, respectively, modulo . It is known that if the multiplicative order of 2Expand
ON ELITE PRIMES OF PERIOD FOUR
A prime p is elite if all sufficiently large Fermat numbers Fn = 22n + 1 are quadratic nonresidues modulo p. In contrast, p is anti-elite if all sufficiently large Fn are quadratic residues modulo p.Expand
THE PRIMITIVE ROOT THEOREM
A primitive root g modulo n is when the congruence gx ≡ 1 (mod n) holds if x = φ(n) but not if 0 < x < φ(n), where φ(n) is the Euler’s function. The primitive root theorem identifies all the positiveExpand
WON Series in Discrete Mathematics and Modern Algebra Volume 6 FROM GROUPS TO GALOIS
These notes are prepared for the students at Philadelphia University in Jordan who are taking the Math 342–442 series of Abstract Algebra. Topics in group theory are covered in the first thirteenExpand
Smith Multiples of a Class of Primes with Small Digital Sum
Using prime numbers whose digits are zeros and ones, we demonstrate how to construct integers \$m\$ for which \$mP\$ is a Smith number for any prime \$P\$ with a fixed, small digital sum. Conversely, usingExpand
WON Series in Discrete Mathematics and Modern Algebra Volume 7 FINITE ABELIAN GROUPS
We detail the proof of the fundamental theorem of finite abelian groups, which states that every finite abelian group is isomorphic to the direct product of a unique collection of cyclic groups ofExpand
Modular zero divisors of longest exponentiation cycle
We show that the sequencew k mod n, given that gcd(w;n) > 1, can reach a maximal cycle length of (n) if and only ifn is twice an odd prime power,w is even, andw is a primitive root modulon=2.
# A 66 INTEGERS 14 ( 2014 ) SMITH NUMBERS WITH EXTRA DIGITAL FEATURES
Using a recently introduced technique, we construct a new infinite sequence of Smith numbers which are palindromic and divisible by their digital sum.
Theory of Numbers
Smith Numbers With Extra Digital Features
• Amin Witno
• Mathematics, Computer Science
• Integers
• 2014