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Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...

Given relatively prime integers p and q (i.e., (p,q)=1), the Dedekind sum is defined by s(p,q)=sum_(i=1)^q((i/q))(((pi)/q)), (1) where ((x))={x-|_x_|-1/2 x not in Z; 0 x in ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

Hoffman (1998, p. 90) calls the sum of the exponents in the prime factorization of a number its roundness. The first few values for n=1, 2, ... are 0, 1, 1, 2, 1, 2, 1, 3, 2, ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...

RSA numbers are difficult to-factor composite numbers having exactly two prime factors (i.e., so-called semiprimes) that were listed in the Factoring Challenge of RSA ...

A generalization by Kronecker of Kummer's theory of prime ideal factors. A divisor on a full subcategory C of mod(A) is an additive mapping chi on C with values in a ...

Two numbers are heterogeneous if their prime factors are distinct. For example, 6=2·3 and 24=2^3·3 are not heterogeneous since their factors are each (2, 3).