fameatop wrote:
What is the remainder when ((55)^15!)^188 is divided by 17?
A) 1
B) 16
C) 3
D) 5
E) 15
((55)^15!)^188
When 55 is divided by 17, the remainder is 4
because we are interested in remainder, we can reduce the previous question as(4^15!)^188
15! will be a even number, so we can safely divide 15! by 2 & raise the power of 4 by 2i.e.
={16^(15!/2)}^188
={[17-1]^(15!/2)}^188
={[-1] ^(15!/2)}^188
Negative 1 raised to any even power will reduce to +1
={1}^188
=1
Thus the remainder is 1
So the answer is
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