Prove the divisibility of the following numbers:

Question

8^10−8^9−8^8 by 55

Answer 1

55 = 5 * 11

8^10−8^9−8^8 = 8^8 * [ 8^2 - 8 - 1] = 64 - 9 = 55 remarkable :)

Answer 2

8^8(8^2 -8 -1)
=8^8(64 - 8 - 1)
= 8^8(55)
which is clearly divisible by 55

Answer 3

Not sure how remarkable it is. It has to be divisible by something.

Answer 4

[Note: I will add the ^ sign, and that just means exponent.]
We know that 8^8(8^2 -8 -1).
Now, simplify.
8^8(64 - 8 - 1)
--------------
8^8 = 55
Now, we know that 8 to the power of 8 is 55 after solving our equation. There's your answer! 8^8*55 proves the divisibility.
ANS - 8^8

Answer 5

Edit - I made a mistake in my other answer.
[Note: I will add the ^ sign, and that just means exponent.]
We know that 8^8(8^2 -8 -1).
Now, simplify.
8^8(64 - 8 - 1)
--------------
8^8 * 55
Now, we know that 8 to the power of 8 is 55 after solving our equation. There's your answer! 8^8*55 proves the divisibility.
ANS - 8^8