We need to find the remainder when ((17)^10)^123) is divided by 3

As you suggested let us divide, 17/3 and feed in the remainder back into the question.

((2)^10)^123)= (1024)^123/3

You can divide 1024 by 3. The remainder is 1. Hence 1^123=1

This was possible because the remainder of 17/3 was a small number,2

Another way of doing this is

((2)^10)^123)=((3-1)^10)^123

When you divide the data inside the bracket by 3, 3 would get completely divided by 3 and hence can be ignored.

((-1)^10)^123

Any negative number raised to an even integer= positive number

1^123=1

Hope that helps!

[quote="Richard0715"]Thanks Kris, I appreciated it! I am just trying to apply the concept to something else but how would I go about this problem? What is the remainder when ((17)^10)^123) is divided by 3? 17/3 has a remainder of 2, feeding in 2 into the problem how would I then find the remainder? Thanks again!

_________________

Thanks

Kris

Instructor at Aspire4GMAT

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