Find the remainder when 54124 is divided by 17.
A. 8
B. 13
C. 16
D. 9
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \frac{{{{54}^{124}}}}{{17}} \cr & Or,\,\frac{{{{\left( {17 \times 3 + 3} \right)}^{124}}}}{{17}} \cr & {\text{The}}\,{\text{remainder}}\,{\text{would}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{{3^{124}}}}{{17}} \cr & Or,\,\frac{{{3^{4 \times 31}}}}{{17}} \cr & {\text{Remainder}}\,{\text{will}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{{3^4}}}{{17}} \cr & Or,\,\frac{{81}}{{17}} \cr & \text{Remainder} = 13 \cr} $$Join The Discussion
Comments ( 5 )
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Ans is 4 ??
What is the correct explaination of this
ans =4
Answer is 4 which is not even in the options & that's wow
I can't the same remainder by totient method. Why ?