Find the remainder when 54¹²⁴ is divided by 17.

Solution (By Examveda Team)

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