Question

Prove that the value of the expression:
165+164 is divisible by 17

Answer 1

`16^(2) (272)` is divisible by 17

Proof:

In order to solve this question we will have to factor
`16^(5) + 16^(4)`. We will have to do that as follows.

`16^(5) + 16^(4) = 16^(3) (16^(2) + 16) = 16^(2) (272)`

From here we know the the resulting number will be equal to
`16^(2) (272)` now we will need to know the following property. If "b" is divisible by "c" then "ab" (where a is any integer) will also be divisible by c. In our case one of the factors is 272, and it is divisible by 17, so that means that
`16^(2) (272)` will also be divisible by 17.

Answer 2

329 divided by 17 is 19.3529411765 so round it 19.3529 turns in to 19.353

so take that and mutiply it by 17 then you will get 329

Explanation: