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Prove that if d divides n then phi(d) divides phi(n).
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Thanks
squelchy451 said:I'm making a quick comment
Euler's totient function IS multiplicative. Someone said it's only for coprimes but there's a general form where the 2 numbers don't have to be coprime
phi(mn) = phi(m)phi(n) * d/phi(d)
where d is the GCD of m and n.
Euler's phi function, also known as the totient function, is a mathematical function that counts the number of positive integers less than or equal to a given number that are relatively prime to it. In other words, it determines the number of positive integers that are coprime (have no common factors) with the given number.
Euler's phi function is significant in number theory, as it has many applications in cryptography, particularly in the RSA algorithm. It is also used in the study of prime numbers and in solving various mathematical problems.
The value of Euler's phi function for a given number n is calculated by finding the prime factorization of n and using the formula φ(n) = n(1-1/p1)(1-1/p2)...(1-1/pk), where p1,p2,...,pk are the distinct prime factors of n.
Euler's phi function is closely related to division, as it is used to determine the number of numbers that are relatively prime to a given number, which is essentially a form of division. It is also used in modular arithmetic, which involves division with remainders.
Euler's phi function has various real-life applications, such as in cryptography for secure communication, in determining the order of elements in a group, and in determining the number of primitive roots of a prime number. It is also used in various mathematical puzzles and problems.