Congruence Theorems in the past, present, and future

in For the Learning of Mathematics (in press)

Rubik's Snakes on a plane

in College Mathematics Journal (in press)

Congruence theorems for convex polygons involving sides, angles, and diagonals

in International Journal of Geometry (2023), 12(2023), 83-92

Minorities in Mathematics

Article for general public (2022)

Der 50cm lange Gliedermaßstab

in Beiträge zum Mathematikunterricht 2022 (Tagungsband GDM) (2022)

Proportionalitätsrechner für Menschen mit einer Dyskalkulie

Scientific Conference (2022)

Sharing calculations to understand arithmetical algorithms and parallel computing

in Mathematics Teacher (2022)

Arithmetic Billiards

in Recreational Mathematics Magazine (2022)

Every number is the beginning of a power of 2

Article for general public (2021)

The degree of Kummer extensions of number fields

in International Journal of Number Theory (2021)

Let K be a number field, and let \alpha_1, ... , \alpha_r be elements of K* which generate a subgroup of K* of rank r. Consider the cyclotomic-Kummer extensions of K given by K(\zeta_n, \sqrt[n_1]{\alpha ... [more ▼]

Let K be a number field, and let \alpha_1, ... , \alpha_r be elements of K* which generate a subgroup of K* of rank r. Consider the cyclotomic-Kummer extensions of K given by K(\zeta_n, \sqrt[n_1]{\alpha_1}, ... , \sqrt[n_r]{\alpha_r}), where n_i divides n for all i. There is an integer x such that these extensions have maximal degree over K(\zeta_g, \sqrt[g_1]{\alpha_1}, ... , \sqrt[g_r]{\alpha_r}), where g=\gcd(n,x) and g_i=\gcd(n_i,x). We prove that the constant x is computable. This result reduces to finitely many cases the computation of the degrees of the extensions K(\zeta_n, \sqrt[n_1]{\alpha_1}, ... , \sqrt[n_r]{\alpha_r}) over K. [less ▲]