QUESTION FOR SSC , UPSC , CDS AND ALL GENERAL COMPETITIONS
Find the remainder when (3^27) is divided by 5? Firstly we will separate 3^27 like this, (3^26).3 (it means 3^27 only) Then, We can also write 3^26 as ((3^2)^13) We just splitted the power of 3 Now, {((3^2)^13).3}/5.......... (i) If we divide 3^2 i.e. 9 by 5 remainder comes to be 4 And that means 4^13 and 4 is less than 5 so remainder again comes to be ( -1) and (-1)^13 means -1 and in eq (i) 3 is also there left to be divided by 5 and hence there is no power on 3 so remainder will also be 3 Atlast we have {(-1)*3}/5 -3/5 means 5-3=2 (if there is - sign in the numerator then we have to substract the numerator from denominator only if numerator is smaller than denominator) So, 2 will be the remainder of this question. FIND THE REMAINDER WHEN 3^1000 IS DIVIDED...