Remainder=?
2 Answers
This can be calculated in a number of ways. One way using brute force is
27^1/7 has a remainder=6 .....(1)
27^2/7=729/7 has a remainder=1 .....(2)
27^3/7=19683/7 has a remainder=6 …….. (3)
27^4/7=531441/7 has a remainder=1 ….. (4)
27^5/7=14348907/7 has a remainder=6 …..(5)
27^6/7=387420489/7 has remainder=1 …. (6)
As as per emerging pattern we observe that the remainder is
Given exponent is
Alternate solution
Explanation:
Given number needs to be divided by
(27)^999
=>(28-1)^999
In the expansion of this series, all terms which have various powers of
We see that this term
Since remainder can not be
This will leave remainder as