Question

Сколько имеется несократимых правильных дробей со знаменателем 123?

Answer 1

Числа 4:5:6:7:8:9
то те которые несократимые,а сократимые 1,3

Answer 2

Number of Irreducible Fractions with Denominator 123

The number of irreducible fractions with a denominator of 123 can be calculated using Euler's totient function, which gives the number of positive integers less than or equal to a given integer that are relatively prime to it. In this case, the number of irreducible fractions with a denominator of 123 is given by φ(123).

Euler's totient function, denoted as φ(n), can be calculated 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.

Using this formula, we can calculate the number of irreducible fractions with a denominator of 123.

The prime factorization of 123 is: 123 = 3 * 41

Therefore, the number of irreducible fractions with a denominator of 123, denoted as φ(123), can be calculated as: φ(123) = 123 * (1 - 1/3) * (1 - 1/41)

Calculating this gives us the number of irreducible fractions with a denominator of 123.