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  1. Number theory | Definition, Topics, & History | Britannica

    Nov 20, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of …

  2. Mathematics - Number Theory, Algorithms, Equations | Britannica

    Nov 11, 2025 · Beginning with Nicomachus of Gerasa (flourished c. 100 ce), several writers produced collections expounding a much simpler form of number theory. A favourite result is the representation …

  3. number theory summary | Britannica

    number theory, Branch of mathematics concerned with properties of and relations among integers. It is a popular subject among amateur mathematicians and students because of the wealth of seemingly …

  4. Number theory - Euclid, Prime Numbers, Divisibility | Britannica

    Nov 20, 2025 · As mathematics filtered from the Islamic world to Renaissance Europe, number theory received little serious attention. The period from 1400 to 1650 saw important advances in geometry, …

  5. Law of large numbers | Probability, Sampling & Estimation | Britannica

    Nov 28, 2025 · Law of large numbers, in statistics, the theorem that, as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their …

  6. Modular arithmetic | Number Theory, Congruence & Algorithms

    Nov 12, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of …

  7. Binomial theorem | Formula & Definition | Britannica

    Nov 19, 2025 · Isaac Newton discovered about 1665 and later stated, in 1676, without proof, the general form of the theorem (for any real number n), and a proof by John Colson was published in 1736.

  8. Number theory - Prime, Distribution, Theorem | Britannica

    Nov 20, 2025 · Number theory - Prime, Distribution, Theorem: One of the supreme achievements of 19th-century mathematics was the prime number theorem, and it is worth a brief digression.

  9. Natural number | Definition & Facts | Britannica

    Nov 19, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of …

  10. Euclidean algorithm | Algorithm, Division & GCD | Britannica

    Sep 16, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of …