Question

Натуральные числа a и b таковы, что 31а=54бА и б составные?

Answer 1

31 нет а 54да такой ответ мой

Answer 2

Natural Numbers and Primality

To determine whether the natural numbers \(a\) and \(b\) are composite, we first need to understand the properties of natural numbers and the concept of compositeness.

Natural Numbers: Natural numbers are the set of positive integers, starting from 1 and extending infinitely. They are commonly denoted by the symbol \(\mathbb{N}\).

Composite Numbers: A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself. In other words, a composite number has factors other than 1 and the number itself.

Equation Analysis

The given equation is \(31a = 54b\). To determine whether \(a\) and \(b\) are composite, we can analyze the properties of the numbers involved in the equation.

Analysis of 31a = 54b

The equation \(31a = 54b\) suggests a relationship between the two natural numbers \(a\) and \(b\). To determine the compositeness of \(a\) and \(b\), we can consider the prime factorization of the numbers involved.

Prime Factorization: Prime factorization is the process of expressing a composite number as a product of prime numbers.

Prime Factorization of 31 and 54

- 31: - 31 is a prime number, as it has no divisors other than 1 and itself. - Therefore, the prime factorization of 31 is simply 31.

- 54: - The prime factorization of 54 is 2 * 3 * 3 * 3 * 2, which can be expressed as \(2^1 * 3^3\).

Conclusion

Given the prime factorization of 31a and 54b, we can conclude that the compositeness of \(a\) and \(b\) depends on their individual prime factorization. Since 31 is a prime number and 54 is composite, the compositeness of \(a\) and \(b\) is determined by the prime factorization of \(b\).

Therefore, based on the given equation \(31a = 54b\), the compositeness of \(a\) and \(b\) is contingent upon the prime factorization of \(b\).