Question

PLEASE HELP! Need this QUICK! This is worth 15 points! Also, will mark brainliest! Thx so much :)

Provide the divisibility for:

7^6+7^5-7^4 by 11

5^5-5^4+5^3 by 7

Thanks again!

Answer 1

Answer:

i used a scientific calculator for these!

if they are wrong please tell me :)

1) 134237.727273

2) 2517.85714286

Answer 2

Answer:

11 does divide (7^6+7^5-7^4) into 5

7 does divide (5^5-5^4+5^3) into 3

Step-by-step explanation:

I don't know what method your teacher wants you to use but am assuming no calculators are allowed. To solve this I would first do some thinking:

(I write 11 divides x as 11|x):

$11|7^6+7^5-7^4=11|7^4(7^2+7-1)$

We can for sure tell that 11 does not divide the factor 7^4 because 7 is prime and so tough luck. but the remaining factor is more amenable

$11|7^2+7-1=11|55$

ad so, clearly, 11 divides the second factor into 5.

As for the second expression, similar thing:

$7|5^5-5^4+5^3=7|5^3(5^2-5+1)$

Again, 5 is prime, so 7 won't ever, never divide 5^3. Second term:

$7|5^2-5+1=7|21$

means 7 divides the expression to 3!