We are given n boxes, labeled 1, 2, . . . , n. Box i weighs i grams and can support a total weight of i grams. The number of different ways to build a single stack of boxes in which no box will be squashed by the weight of the boxes above it is denoted by f(n). In a 2006 paper, the first author asked for “congruences for f(n) modulo high powers of 2”. In this note, we accomplish this task by pr...

Classroom assessment tasks and environment are central to supporting student learning, yet are under-studied at the tertiary level, especially in China’s test-driven culture. This study explores the relationship between students’ perceptions of assessment tasks and classroom assessment environment, within the university context of teaching English as a foreign language (EFL) in China. A questio...

The Fermat and Solovay–Strassen tests are each based on translating a congruence modulo prime numbers, either Fermat’s little theorem or Euler’s congruence, over to the setting of composite numbers and hoping to make it fail there. The Miller–Rabin test uses a similar idea, but involves a system of congruences. For an odd integer n > 1, factor out the largest power of 2 from n− 1, say n− 1 = 2e...

Abstract The underrepresentation of women in leadership positions persists. Existing research examines barriers face climbing organizational hierarchies, but we know less about who break past the glass ceiling. Once obtain supervisory positions, do they additional hurdles managing employees? Specifically, how does gender, gender congruence, and rule formalization influence employee compliance t...

For distributive double p-algebras, a close connection is established between being congruence coherent and congruence regular. Every congruence regular distributive double p-algebra is congruence coherent. Even though every congruence coherent distributive double p-algebra that has either a non-empty core or finite range is congruence regular, an example is given that is congruence coherent bu...