Question

Доказать, что 8^8-8^7+8^6 делится на 57.

Answer 1

Ответ:

Объяснение:

Што означає ^

Answer 2

To prove that $8^8 - 8^7 + 8^6$ is divisible by 57, we need to show that the difference $8^8 - 8^7 + 8^6$ leaves no remainder when divided by 57.

To do this, we'll use modular arithmetic, specifically properties related to divisibility. A number $a$ is divisible by $b$ if and only if $a \equiv 0 \mod b$, which means $a$ leaves no remainder when divided by $b$.

Let's simplify the expression $8^8 - 8^7 + 8^6$:

$8^8 - 8^7 + 8^6 = 8^6(8^2 - 8 + 1)$.

Now, we know that $8^2 = 64$. Let's check if $64 - 8 + 1$ is divisible by 57:

$64 - 8 + 1 = 57$.

As we can see, $64 - 8 + 1$ is equal to 57, which means it is divisible by 57. Therefore, the entire expression $8^8 - 8^7 + 8^6$ is also divisible by 57.

Thus, we have proven that $8^8 - 8^7 + 8^6$ is divisible by 57.