Question

Делится ли число 99^3-53^3 на 23? Ответ поясните.

Answer 1

99³-53³=(99-53)(99²+99*53+53²)=46(99²+99*53+53²)=23*2(99²+99*53+53²)   
Да, делится. Т. к. есть множитель 23.

Answer 2

99:3=33
53:3=17,6
23:3=7,6

Answer 3

To determine if the number $99^3 - 53^3$ is divisible by 23, we need to check if the remainder of the division is zero. In other words, we need to verify if $(99^3 - 53^3) \mod 23 = 0$.

Now, let's calculate $99^3$ and $53^3$ first:

$99^3 = 99 \times 99 \times 99 = 970,299$.

$53^3 = 53 \times 53 \times 53 = 148,877$.

Next, we need to find the difference $(99^3 - 53^3)$:

$99^3 - 53^3 = 970,299 - 148,877 = 821,422$.

Now, we need to check if $821,422$ is divisible by 23. To do this, we calculate the remainder of the division $821,422 \div 23$:

$821,422 \div 23 = 35,702$ with a remainder of $12$.

Since the remainder is not zero (it's $12$), the number $99^3 - 53^3$ is not divisible by 23.

In summary, $99^3 - 53^3$ is not divisible by 23, and the remainder of the division is 12.