Examveda
Examveda

Find the remainder when 54124 is divided by 17.

A. 8

B. 13

C. 16

D. 9

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & \frac{{{{54}^{124}}}}{{17}} \cr & Or,\,\frac{{{{\left( {17 \times 3 + 3} \right)}^{124}}}}{{17}} \cr & {\text{The}}\,{\text{remainder}}\,{\text{would}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{{3^{124}}}}{{17}} \cr & Or,\,\frac{{{3^{4 \times 31}}}}{{17}} \cr & {\text{Remainder}}\,{\text{will}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{{3^4}}}{{17}} \cr & Or,\,\frac{{81}}{{17}} \cr & \text{Remainder} = 13 \cr} $$

This Question Belongs to Arithmetic Ability >> Number System

Join The Discussion

Comments ( 5 )

  1. Electronics Telecommunication
    Electronics Telecommunication :
    1 year ago

    Ans is 4 ??

  2. Electronics Telecommunication
    Electronics Telecommunication :
    1 year ago

    What is the correct explaination of this

  3. Technical Aman
    Technical Aman :
    4 years ago

    ans =4

  4. Mohd Faijan
    Mohd Faijan :
    5 years ago

    Answer is 4 which is not even in the options & that's wow

  5. Baadshah Baadshah
    Baadshah Baadshah :
    5 years ago

    I can't the same remainder by totient method. Why ?

Related Questions on Number System