Remainder estimates for squarefree integers in arithmetic progression

On primitive sets of squarefree integers

On Integers Nonrepresentable by a Generalized Arithmetic Progression

We consider those positive integers that are not representable as linear combinations of terms of a generalized arithmetic progression with nonnegative integer coefficients. To do this, we make use of the numerical semigroup generated by a generalized arithmetic progression. The number of integers nonrepresentable by such a numerical semigroup is determined as well as that of its dual. In addit...

Integers without divisors from a fixed arithmetic progression

Let a be an integer and q a prime number. In this paper we find an asymptotic formula for the number of positive integers n ≤ x with the property that no divisor d > 1 of n lies in the arithmetic progression a modulo q. MSC numbers: 11A05, 11A25, 11N37

A Possible New Quantum Algorithm: Arithmetic with Large Integers via the Chinese Remainder Theorem

Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from most quantum algorithms currently under discussion in that the output would presumably be obtained by classical superposition of the output of many identical...

Squarefree Integers without Large Prime Factors in Short Intervals