Question

Исмаил утверждает что если число m-любое простое число большее 3,тогда двучлен m^2 - 1 полностью делится на 12.по-вашему это предложение верно? а)Верность предложения ,проверьте, поставив в место m любое простое число б)разложите двучлен m^2 - 1 на множители .Выясните почему полученное произведение делится на 4. Как можно обосновать деление этого произведения на 3? Назовите полученный результат. Срочно сделайте!!! ДАЮ 50 БАЛЛОВ СРОЧНО, ЗАРАНИЕ ЗДЕЛАЙТЕ

Answer 1

Тут надо решать часа 2

Answer 2

Verifying Ismail's Claim about Prime Numbers and Divisibility

Ismail claims that if the number m is any prime number greater than 3, then the expression m^2 - 1 is completely divisible by 12. Let's verify this claim.

Testing the Claim with a Prime Number

To verify the claim, let's substitute a prime number greater than 3 in place of m and check if the expression m^2 - 1 is divisible by 12.

Let's take the prime number 5 and substitute it into the expression: 5^2 - 1

Factoring the Expression

Now, let's factor the expression m^2 - 1 and understand why the resulting product is divisible by 4. Additionally, we'll explore how to justify the division of this product by 3 and state the obtained result.

The expression m^2 - 1 can be factored as: m^2 - 1 = (m + 1)(m - 1)

Divisibility by 4

The product of two consecutive numbers is always even, and one of them is always divisible by 2. Therefore, the product (m + 1)(m - 1) is always divisible by 2, and hence, by 4.

Justifying Division by 3

To justify the division of the product (m + 1)(m - 1) by 3, we can use the fact that for any three consecutive numbers, one of them is always divisible by 3. Therefore, in the product (m + 1)(m - 1), one of the factors will be divisible by 3, making the entire product divisible by 3.

Conclusion

After substituting m = 5 into the expression m^2 - 1, we find that the resulting product is indeed divisible by 12, confirming Ismail's claim.

I hope this explanation helps! If you have further questions or need additional assistance, feel free to ask.