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src/algebra/all-submasks.md

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title: Submask Enumeration
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# Submask Enumeration
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## Enumerating all submasks of a given mask

src/algebra/balanced-ternary.md

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title: Balanced Ternary
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# Balanced Ternary
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!["Setun computer using Balanced Ternary system"](http://ternary.3neko.ru/photo/setun1_small.jpg)

src/algebra/big-integer.md

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title: Arbitrary
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# Arbitrary-Precision Arithmetic
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Arbitrary-Precision arithmetic, also known as "bignum" or simply "long arithmetic" is a set of data structures and algorithms which allows to process much greater numbers than can be fit in standard data types. Here are several types of arbitrary-precision arithmetic.

src/algebra/binary-exp.md

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title: Binary Exponentiation
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# Binary Exponentiation
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Binary exponentiation (also known as exponentiation by squaring) is a trick which allows to calculate $a^n$ using only $O(\log n)$ multiplications (instead of $O(n)$ multiplications required by the naive approach).

src/algebra/chinese-remainder-theorem.md

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title: Chinese Remainder Theorem
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# Chinese Remainder Theorem
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The Chinese Remainder Theorem (which will be referred to as CRT in the rest of this article) was discovered by Chinese mathematician Sun Zi.

src/algebra/discrete-log.md

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title: Discrete Logarithm
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# Discrete Logarithm
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The discrete logarithm is an integer $x$ satisfying the equation

src/algebra/discrete-root.md

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title: Discrete Root
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# Discrete Root
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The problem of finding a discrete root is defined as follows. Given a prime $n$ and two integers $a$ and $k$, find all $x$ for which:

src/algebra/divisors.md

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# Number of divisors / sum of divisors
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In this article we discuss how to compute the number of divisors $d(n)$ and the sum of divisors $\sigma(n)$ of a given number $n$.

src/algebra/euclid-algorithm.md

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title: Euclidean algorithm for computing the greatest common divisor
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# Euclidean algorithm for computing the greatest common divisor
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Given two non-negative integers $a$ and $b$, we have to find their **GCD** (greatest common divisor), i.e. the largest number which is a divisor of both $a$ and $b$.

src/algebra/extended-euclid-algorithm.md

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title: Extended Euclidean Algorithm
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# Extended Euclidean Algorithm
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While the [Euclidean algorithm](euclid-algorithm.md) calculates only the greatest common divisor (GCD) of two integers $a$ and $b$, the extended version also finds a way to represent GCD in terms of $a$ and $b$, i.e. coefficients $x$ and $y$ for which:

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