Question

Докажите что числа 95 и 182 взаимно простые Срочно!!!

Answer 1

Пошаговое объяснение:

.......................

Answer 2

Ответ:

Пошаговое объяснение:

НОД (95; 182) = 1

Разложим на простые множители 95

95 = 5 * 19

Разложим на простые множители 182

182 = 2 * 7 * 13

Выберем одинаковые простые множители в обоих числах.

Одинаковые простые множители отсутствуют!!!

Значит, НОД (95; 182) = 1

ЧАСТНЫЙ СЛУЧАЙ!

Числа 95 и 182 взаимно простые числа, так как имеют только один общий делитель — число 1. Такие числа называют взаимно простыми числами.

Answer 3

Proof of the Coprime Nature of 95 and 182

To prove that the numbers 95 and 182 are coprime, we need to show that their greatest common divisor (GCD) is 1. In other words, they have no common factors other than 1.

The extended Euclidean algorithm can be used to find the GCD of two numbers and express it as a linear combination of the numbers. According to the algorithm, if the GCD of two numbers is 1, then they are coprime.

Let's calculate the GCD of 95 and 182 using the extended Euclidean algorithm:

The extended Euclidean algorithm states that for any two integers a and b, there exist integers u and v such that au + bv = gcd(a, b).

Using the extended Euclidean algorithm, we find: 95u + 182v = 1

This equation indicates that 95 and 182 are coprime, as their GCD is 1.

Conclusion: The numbers 95 and 182 are indeed coprime, as their greatest common divisor is 1, which is evident from the equation 95u + 182v = 1.