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About 4,264 papers for “Modular arithmetic”

Modular Arithmetic

Daniel I. Rosenthal, David I. Rosenthal, Peter Rosenthal · Undergraduate texts in mathematics · 2014

Cited by 0

Modular arithmetic

Moretti, Christopher · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2011

This visually illustrates various properties of modular arithmetic by creating an "operation table" modulo n, where 0 is represented by black, 1 by white, and other values by intermediate colors. The allowed numbers can be restricted to be nonzero or the units modulo n, and the operations are modular addition, subtraction, powers, and sums of squares

Cited by 0

modular arithmetic

Mahdi Tahar Brahimi · Zenodo (CERN European Organization for Nuclear Research) · 2026

Cited by 0Open access

Modular arithmetic

Davidson, Kenneth, Satriano, Matthew · Mathematical world · 2023

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Modular Arithmetic

Lindsay N. Childs · Springer undergraduate texts in mathematics and technology · 2019

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Modular Arithmetic

Afroz Afroz · 2019

The integer arithmetic is indispensable at most every area such as cryptology, computer graphics, mathematics, and several other engineering areas. Number theory is a branch of pure mathematics which helps to analyze and study the integers. It is partly experimental and partly theoretical. The chapter presents integers and its arithmetic operations on a number line, modules arithmetic with examples, additive inverse, matrix, linear congruence, a solution of linear congruence, prime and relatively prime number, GCDs with examples to cover all content tasks. An integer can be represented along a number line by an arrow. A positive number is represented by an arrow pointing to the right. The theoretical part tries to device an argument that gives a conclusive answer to the questions.

Cited by 1

Modular Arithmetic

Jeffrey Stopple · Cambridge University Press eBooks · 2003

Traditional books on number theory that emphasize the algebraic aspects begin with the subject of modular arithmetic. This is a very powerful technique, based on the work of Fermat, Euler, and Gauss. The idea is to fix an integer, n, and group all the rest of the integers into one of n classes, depending on what remainder you get when you divide by n. A more elegant way of saying this is that two integers, a and b, are in the same class if n divides b − a or, in other words, b − a is an integer multiple of n. In this case, we write a ≡ b mod n. (This is pronounced “a is congruent to b modulo n.”) For example, with n = 6, 5 ≡ 17 mod 6, −2 ≡ 4 mod 6, and even 6 ≡ 0 mod 6. Because there are seven days in a week, the fact that 3 ≡ 10 mod 7 means that the 3rd of the month and the 10th of the month fall on the same weekday.

Cited by 0

Modular Arithmetic

Ulrich Daepp, Pamela Gorkin · Undergraduate texts in mathematics · 2026

Cited by 0