Question

Докажите что 3^13-3^10-3^9 делится на 77Помогите пожалуйста​

Answer 1

Ответ:

Объяснение:

Смотри

Answer 2

Объяснение:

$3^{13}-3^{10}-3^9=3^9*(3^4-3-1)=3^9*(81-3-1)=77*3^9.$

Answer 3

To prove that the expression 3^13 - 3^10 - 3^9 is divisible by 77, we can use modular arithmetic.

Modular arithmetic is a system of arithmetic for integers where numbers "wrap around" after reaching a certain value called the modulus. In this case, the modulus is 77.

To show that the expression is divisible by 77, we need to demonstrate that it leaves a remainder of 0 when divided by 77.

Let's break down the expression step by step:

1. 3^13 - 3^10 - 3^9

First, let's simplify each term individually:

2. 3^13 = 1594323 3. 3^10 = 59049 4. 3^9 = 19683

Now, substitute these values back into the original expression:

5. 1594323 - 59049 - 19683

Next, let's simplify the expression further:

6. 1594323 - 59049 - 19683 = 1528591

Now, we need to check if 1528591 is divisible by 77. To do this, we can calculate the remainder when 1528591 is divided by 77.

7. 1528591 % 77 = 0

The remainder is 0, which means that 1528591 is divisible by 77. Therefore, we can conclude that the expression 3^13 - 3^10 - 3^9 is divisible by 77.

Please let me know if you have any further questions!