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eul

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There are 3 letters in EUL ( E¹L¹U¹ )

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Definitions of eul in various dictionaries:

EUL - In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using t...

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Eul might refer to
In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as φ(n) or ϕ(n), and may also be called Euler's phi function. It can be defined more formally as the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes referred to as totatives of n. * For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, because gcd(9, 3) = gcd(9, 6) = 3 and gcd(9, 9) = 9. Therefore, φ(9) = 6. As another example, φ(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1. * Euler's totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then φ(mn) = φ(m)φ(n). * This function gives the order of the multiplicative group of integers modulo n (the group of units of the ring ℤ/nℤ). It also plays a key role in the definition of the RSA encryption system.

Eul might refer to

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as φ(n) or ϕ(n), and may also be called Euler's phi function. It can be defined more formally as the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes referred to as totatives of n.
* For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, because gcd(9, 3) = gcd(9, 6) = 3 and gcd(9, 9) = 9. Therefore, φ(9) = 6. As another example, φ(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1.
* Euler's totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then φ(mn) = φ(m)φ(n).
* This function gives the order of the multiplicative group of integers modulo n (the group of units of the ring ℤ/nℤ). It also plays a key role in the definition of the RSA encryption system.

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