Question

Сколько имеется несокротимых дробей со знаменателем 145?

Answer 1

224(112 положительных и 112 отрицательных)

Answer 2

Count of Irreducible Fractions with Denominator 145

To find the count of irreducible fractions with a denominator of 145, we can use the formula for Euler's totient function, which gives the number of positive integers less than or equal to n that are relatively prime to n. In this case, we can use Euler's totient function to find the count of irreducible fractions with a denominator of 145.

The formula for Euler's totient function is given by: φ(n) = n * (1 - 1/p1) * (1 - 1/p2) * ... * (1 - 1/pk), where p1, p2, ..., pk are the distinct prime factors of n.

Using this formula, we can calculate the count of irreducible fractions with a denominator of 145.

The prime factorization of 145 is 5 * 29. Therefore, the count of irreducible fractions with a denominator of 145 can be calculated using Euler's totient function as follows: φ(145) = 145 * (1 - 1/5) * (1 - 1/29)

Let's calculate the value of φ(145) using the formula.

φ(145) = 145 * (1 - 1/5) * (1 - 1/29) φ(145) = 145 * (4/5) * (28/29) φ(145) = 145 * (112/145) φ(145) = 112

Therefore, there are 112 irreducible fractions with a denominator of 145.