Definitions for euler's totient function
eu·ler's to·tient func·tion

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1. Euler's totient function

   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 ) {\displaystyle \varphi (n)} or ϕ ( n ) {\displaystyle \phi (n)} , and may also be called Euler's phi function. In other words, it is 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, since 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 / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } ). It is also used for defining the RSA encryption system.

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1. Euler's totient function

   In number theory, Euler's totient or phi function, φ is an arithmetic function that counts the number of positive integers less than or equal to n that are relatively prime to n. That is, if n is a positive integer, then φ is the number of integers k in the range 1 ≤ k ≤ n for which gcd = 1. The totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then φ = φφ. For example let n = 9. Then gcd = gcd = 3 and gcd = 9. The other six numbers in the range 1 ≤ k ≤ 9, that is, 1, 2, 4, 5, 7 and 8, are relatively prime to 9. Therefore, φ = 6. As another example, φ = 1 since gcd = 1. The totient function is important mainly because it gives the order of the multiplicative group of integers modulo n. See Euler's theorem. The totient function also plays a key role in the definition of the RSA encryption system.

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How to say euler's totient function in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of euler's totient function in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of euler's totient function in Pythagorean Numerology is: 6

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Euler'S_Totient_Function
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=euler's totient function