Abstract. It is well-known that Euclid’s argument can be adapted to prove the infinitude of primes of the form 4k − 1. We describe a simple proof that the sum of the reciprocals of all such primes diverges. More generally, if q is a positive integer, and H is a proper subgroup of the units group (Z/qZ)×, we show that ∑ p prime p mod q 6∈
Let pn denote the nth prime, and consider the function 1/n → 1/pn which maps the reciprocals of the ...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
Leonard Euler tried to prove one of Fermat's most elegant remarks, the Prime number theorem [1, 73]....
Abstract. It is well-known that Euclid’s argument can be adapted to prove the infinitude of primes o...
Abstract. In a 1737 paper, Euler gave the first proof that the sum of the reciprocals of the prime n...
A famous theorem of Weierstrass states that every continuous function on the closed unit interval [0...
Theorem. There are infinitely many primes. Euclid’s proof of this theorem is a classic piece of math...
AbstractWe examine densities of several sets connected with the Fermat numbers Fm=22m+1. In particul...
Fermat’s little theorem is an important property of integers to a prime modulus. Theorem 1.1 (Fermat...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Given Γ⊂Q∗ a multiplicative subgroup and m∈N+ , assuming the Generalized Riemann Hypothesis, we dete...
A rational octic reciprocity theorem analogous to the rational biquadratic reciprocity theorem of Bu...
In this note we give a new proof of the existence of infinitely many prime numbers. There are severa...
Abstract Let \(ξ\) and \(m\) be integers satisfying \(ξ \ne 0\) and \(m ≥ 3\). We show that for any...
In this paper we prove that there exist infInitely many disjoint sets of posItIve integers which the...
Let pn denote the nth prime, and consider the function 1/n → 1/pn which maps the reciprocals of the ...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
Leonard Euler tried to prove one of Fermat's most elegant remarks, the Prime number theorem [1, 73]....
Abstract. It is well-known that Euclid’s argument can be adapted to prove the infinitude of primes o...
Abstract. In a 1737 paper, Euler gave the first proof that the sum of the reciprocals of the prime n...
A famous theorem of Weierstrass states that every continuous function on the closed unit interval [0...
Theorem. There are infinitely many primes. Euclid’s proof of this theorem is a classic piece of math...
AbstractWe examine densities of several sets connected with the Fermat numbers Fm=22m+1. In particul...
Fermat’s little theorem is an important property of integers to a prime modulus. Theorem 1.1 (Fermat...
Dirichlet’s 1837 theorem that every coprime arithmetic progression a mod m contains infinitely many ...
Given Γ⊂Q∗ a multiplicative subgroup and m∈N+ , assuming the Generalized Riemann Hypothesis, we dete...
A rational octic reciprocity theorem analogous to the rational biquadratic reciprocity theorem of Bu...
In this note we give a new proof of the existence of infinitely many prime numbers. There are severa...
Abstract Let \(ξ\) and \(m\) be integers satisfying \(ξ \ne 0\) and \(m ≥ 3\). We show that for any...
In this paper we prove that there exist infInitely many disjoint sets of posItIve integers which the...
Let pn denote the nth prime, and consider the function 1/n → 1/pn which maps the reciprocals of the ...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
Leonard Euler tried to prove one of Fermat's most elegant remarks, the Prime number theorem [1, 73]....
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