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Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on.
In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different ...
In number theory, an arithmetic, arithmetical, or number-theoretic function [1] [2] is generally any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. [3] [4] [5] Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of ...
Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication, and division) first
Arithmetic is an elementary branch of mathematics that is widely used for tasks ranging from simple day-to-day counting to advanced science and business calculations.
In modular arithmetic (modulo a prime number) and for real numbers, nonzero numbers have a multiplicative inverse. In these cases, a division by x may be computed as the product by the multiplicative inverse of x. This approach is often associated with the faster methods in computer arithmetic.
The fundamental theorem of arithmetic can also be proved without using Euclid's lemma. [13] The proof that follows is inspired by Euclid's original version of the Euclidean algorithm . Assume that s {\displaystyle s} is the smallest positive integer which is the product of prime numbers in two different ways.
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.