Divisibility tests for digits other than 7 are well known and rely on the base 10 representation of numbers. For example, a natural number is divisible by 4 if the last 2 digits are divisible by 4 because 4 divides 10[sup k] for all k equal to or greater than 2. Divisibility tests for 7, while not nearly as well known, do exist and are also…

In this note, using the theory of Pell equation, the authors discuss the integrity of certain series involving generalized Fibonacci and Lucas numbers.

This dissertation explores the robust confluence of syntactic and cultural factors involved in the structure and content of chengyu. It unpacks a number of structural tendencies in the data sample, and illuminates selected underlying cultural themes. The presence of syntactic and semantic parallelism within chengyu, as an expression of the…

Arithmetic tests for divisibility of an integer by another integer are well known. This article states and proves conditions for divisibility in binary form.

The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, "m"th "g -…

Nearly all studies on perception and cognition have used discrete responses to infer internal cognitive processes. In the current study, we demonstrate that visually-guided manual reaching can provide new opportunities to access internal processes over time. In each trial, participants were required to compare a single digit Arabic number…

According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by…

This paper focuses on teaching and learning the set of real numbers "R" and its completeness property at the university level. It studies, in particular, the opportunities for understanding this property that students are offered in four undergraduate correlative courses in Calculus and Analysis. The theoretical framework used in the study draws…

Evidence is presented for 2 modes of attention operating in simultanagnosia. The authors examined visual enumeration in a patient, GK, who has severe impairments in serially scanning across a scene and is unable to count the numbers of items in visual displays. However, GK's ability to judge the relative magnitude of 2 displays was consistently…

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

This study is concerned with the development of children's intuitive understanding of nonlinear processes. The ability to estimate linear and exponential growth was examined in 7-, 9-, 11-, and 13-year-old children and adults (N=160). Whereas linear growth was judged correctly at all ages, estimations of exponential growth were in line with…

This article expresses concern for the sloppy language that is often used by the media to describe numerical comparisons and suggests guidelines for how such comparisons should be described such that the meanings are unambiguous.

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

Developmental dyscalculia (DD) is a deficit in number processing and arithmetic that affects 3-6% of schoolchildren. The goal of the present study was to analyze cerebral bases of DD related to symbolic number processing. Children with DD aged 9-11 years and matched children with no learning disability history were investigated using fMRI. The two…