A Goldbach theorem for polynomials of low degree over odd finite fields
A new modulo computation algorithm
A note on multiplicatively e-perfect numbers.
A number-theoretic conjecture and its implication for set theory.
A quadratic field which is euclidean but not norm-euclidean.
A survey of divisibility tests with a historical perspective.
About division by 1.
An analysis of GCD and LCM matrices via the -factorization.
An awful problem about integers in base four
An improvement of Euclid's algorithm
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
An upper bound for the norm of a gcd-related matrix.
Approximate polynomial GCD
The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications, for example, in image processing and control theory. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and commonly used Euclid’s algorithm. However, this is an ill-posed problem, particularly when some unknown noise is applied to the polynomial coefficients. Hence, new methods for the GCD computation...
Arithmetic progressions in a unique factorization domain
Arithmetic properties of numbers with restricted digits