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Find the remainder when 54¹²⁴ is divided by 17.

18
213
316
49

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{54^{124}}{17} \\ O r, \frac{{(17 \times 3 + 3)}^{124}}{17} \\ The remainder would be same as, \\ \frac{3^{124}}{17} \\ O r, \frac{3^{4 \times 31}}{17} \\ Remainder will be same as, \\ \frac{3^{4}}{17} \\ O r, \frac{81}{17} \\ Re m a i n d e r = 13 \end{aligned}

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

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{54^{124}}{17} \\ O r, \frac{{(17 \times 3 + 3)}^{124}}{17} \\ The remainder would be same as, \\ \frac{3^{124}}{17} \\ O r, \frac{3^{4 \times 31}}{17} \\ Remainder will be same as, \\ \frac{3^{4}}{17} \\ O r, \frac{81}{17} \\ Re m a i n d e r = 13 \end{aligned}

$\eqalign{ & \frac{{{{54}^{124}}}}{{17}} \cr & Or,\,\frac{{{{\left( {17 \times 3 + 3} \right)}^{124}}}}{{17}} \cr & {\text{The}}\,{\text{remainder}}\,{\text{would}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{{3^{124}}}}{{17}} \cr & Or,\,\frac{{{3^{4 \times 31}}}}{{17}} \cr & {\text{Remainder}}\,{\text{will}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{{3^4}}}{{17}} \cr & Or,\,\frac{{81}}{{17}} \cr & \operatorname{Re} mainder = 13 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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