In a positional number system, the numerical value of each symbol depends on its position
in the sequence of digits representing the number. Any integer greater than 1 may serve as …

Representations of Integers as Sums of an Even Number of Squares Page 1 Chapter 9
Representations of Integers as Sums of an Even Number of Squares §1. A Sketch of the …

Let $ k\ge 2$ be an integer and let $ A $ be a set of nonnegative integers. For a $ k $-tuple of
positive integers $\underline {\lambda}=(\lambda_ {1},\dots {},\lambda_ {k}) $ with …

In this paper we revise some previously defined nonpositional number encodings using
multisets and their associated arithmetic operations, describing a general …

We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci
base such that the sum of the absolute values of the digits is minimal. For the Fibonacci …

In a base phi representation a natural number is written as a sum of powers of the golden
mean $\varphi $. There are many ways to do this. How many? Even if the number of powers …

Alternate base numeration systems generalize real base numeration systems as defined by
Renyi. Real numbers are represented using a finite number of bases periodically. Such …

1. Introduction. Let n and r denote integers with r> 0 and let](n) f (n, r) be an arithmetical
function with values in the complex field. We say that f (n, r) is an even (periodic) function of …

Recall that rational numbers are precisely real numbers with repeating decimal expansions.
In this paper, we explore expansions in arbitrary bases and provide an online calculator …

Introduction to decimal, binary and hexadecimal number systems and their inter
conversions, Unsigned and Signed binary number representations, Rules of binary addition …