A Gaussian rational, also known as a Gaussian integer, is a complex number of the form \( a + bi \), where \( a \) and \( b \) are both rational numbers (i.e., they can be expressed as a fraction of integers), and \( i \) is the imaginary unit satisfying \( i^2 = -1 \).

The Manin–Drinfeld theorem is a significant result in the field of algebraic geometry and number theory, particularly in the study of rational points on algebraic curves. It was developed independently by mathematicians Yuri Manin and Vladimir Drinfeld in the 1970s. The theorem deals with the existence and structure of rational points on certain types of algebraic varieties, especially in the context of curves defined over non-closed fields, such as the rational numbers \(\mathbb{Q}\).

Integer sequences are ordered lists of integers. Each integer in the sequence can be distinct or can repeat, and they can follow a specific mathematical rule or pattern. Integer sequences are often studied in various areas of mathematics, including number theory, combinatorics, and combinatorial optimization. Some famous examples of integer sequences include: 1. **Fibonacci Sequence**: A sequence where each number is the sum of the two preceding ones, usually starting with 0 and 1.

A modular unit generally refers to a standardized and interchangeable component or system that can be combined with other modular units to form a larger, more complex structure or functioning system. This concept is applied across various fields, including architecture, manufacturing, software development, and education.

In number theory, the **normal order** of an arithmetic function describes the typical or average asymptotic behavior of the function across integers. More formally, an arithmetic function \( f(n) \) is said to have a normal order \( g(n) \) if, for almost all integers \( n \), \( f(n) \) is approximately equal to \( g(n) \) in a certain sense.

Octic reciprocity is a concept in number theory, particularly in the field of algebraic number theory, which extends the idea of reciprocity laws for quadratic residues (the classical quadratic reciprocity) to higher powers. While the classic quadratic reciprocity law, proven by Carl Friedrich Gauss, deals with the solvability of certain congruences involving squares (i.e., second powers), octic reciprocity focuses on eighth powers.

Index numbers are statistical measures designed to represent the relative change in a variable or a group of variables over time or between different groups. They are widely used in economics and finance to compare the performance of different economic indicators and to analyze trends. Here are some key aspects of index numbers: 1. **Purpose**: Index numbers help in understanding how certain values have changed relative to a base value over a specific period. They simplify complex data and allow for easy comparison.

Udyotakara was an influential Indian philosopher and commentator from the 6th century CE, primarily associated with the tradition of ancient Indian logic and philosophy. He is best known for his work on the Nyaya system, which is one of the six orthodox schools of Hindu philosophy focused on logic, epistemology, and metaphysics.

The Scientific Committee on Oceanic Research (SCOR) is an international organization established to promote and facilitate oceanographic research and related scientific activities. It was founded in 1957 and operates under the auspices of the International Council for Science (ICSU), which is now part of the International Science Council (ISC).

The Second Hardy–Littlewood conjecture, also known as the "2-ary Goldbach conjecture," is an unsolved problem in number theory that is concerned with the representation of even integers as sums of prime numbers. Specifically, it builds upon the ideas found in the original Goldbach conjecture. The conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers.

Numeral systems are methods for expressing numbers in a consistent manner, typically using a set of symbols and a base or radix. Each numeral system has its own rules for representing numerical values. Here are some of the most common numeral systems: 1. **Decimal (Base 10)**: The most commonly used numeral system, employing ten digits (0-9). Each position represents a power of ten.

A number is a mathematical concept that represents a quantity or value. Numbers can be categorized into various types, including: 1. **Natural Numbers**: These are the positive integers starting from 1, 2, 3, and so on (1, 2, 3, ...). 2. **Whole Numbers**: These include all natural numbers and zero (0, 1, 2, 3, ...).

A numeral system is a mathematical notation for representing numbers of a given set, employing a consistent set of symbols and rules for rendering and manipulating them. Numeral systems vary in the way they express numbers, and they can be classified by their base, which indicates how many unique digits are used, including a representation for zero.

The Numero sign, which looks like this: №, is a typographic symbol that denotes "number." It is commonly used to indicate ordinal numbers, typically preceding a numeral. For example, you might see "№ 5" to represent "number 5." The symbol is derived from the Latin word "numero," which means "by number." It is often used in contexts such as specifications, listings, and formal documents to identify items in a numbered sequence.

A numeronym is a type of abbreviation where a word or phrase is represented by its first letter, a number that represents the number of letters omitted, and its last letter. For example, the word "international" can be abbreviated as "i18n" (where "18" denotes the 18 letters between the first letter "i" and the last letter "n").

"Numbers" is an American television series that aired from 2005 to 2010. It was created by Nick Falco and is centered around an FBI agent, Don Eppes, who uses mathematical concepts and equations to help solve crimes, with the assistance of his brother, Charlie Eppes, a brilliant mathematician. The show features a combination of procedural crime-solving and the application of mathematics to real-world problems. Throughout its six seasons, "Numbers" aired a total of 118 episodes.

Nyaya is one of the six āstika (orthodox) schools of Hindu philosophy, which focuses on the study of logic and epistemology. Throughout its history, there has been a significant lineage of philosophers and teachers associated with the Nyaya school.