Question

12^13–12^12+12^11 is divisible by 7 and 19.

Answer 1

Answer:

The statement is true

Step-by-step explanation:

The question is as following :

$12^{13}-12^{12}+12^{11}$ is divisible by 7 and 19, true or false?

The given expression is $12^{13}-12^{12}+12^{11}$

Take $12^{11}$ as a common

$12^{13}-12^{12}+12^{11} = 12^{11}*(12^2-12^1+12^0)\\= 12^{11} *(144-12+1)\\=12^{11} * 133\\= 12^{11} * 7 * 19$

So, $12^{11} * 7 * 19$ divided 7 = $12^{11} * 19$

And $12^{11} * 7 * 19$ divided 19 = $12^{11} * 7$

$12^{13}-12^{12}+12^{11}$ is divisible by 7 and 19 (True)