259255259255\frac{{{2^{59}}}}{{255}} is: " /> 259255259255\frac{{{2^{59}}}}{{255}} is: " /> 259255259255\frac{{{2^{59}}}}{{255}} is: " />

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The remainder of $\frac{2^{59}}{255}$ $\frac{{{2^{59}}}}{{255}}$ is:

155
256
30
4None of these

Answer:- 1

Explanation:-

Solution:

\begin{aligned} 2^{59} can be expressed as 2^{8 n} \\ So, \\ Remainder \frac{2^{59}}{255} \\ = Remainder \frac{2^{8 n}}{255} \\ = Remainder \frac{256^{n}}{255} = 1 \\ Required remainder = 1 \end{aligned}

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is: ", "text": "The remainder of

\frac{2^{59}}{255}

$\frac{{{2^{59}}}}{{255}}$ is: ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} 2^{59} can be expressed as 2^{8 n} \\ So, \\ Remainder \frac{2^{59}}{255} \\ = Remainder \frac{2^{8 n}}{255} \\ = Remainder \frac{256^{n}}{255} = 1 \\ Required remainder = 1 \end{aligned}

$\eqalign{ & {2^{59}}\,{\text{can}}\,{\text{be}}\,{\text{expressed}}\,{\text{as}}\,{2^{8n}} \cr & {\text{So}}, \cr & {\text{Remainder}}\,\frac{{{2^{59}}}}{{255}} \cr & = {\text{Remainder}}\,\frac{{{2^{8n}}}}{{255}} \cr & = {\text{Remainder}}\,\frac{{{{256}^n}}}{{255}} = 1 \cr & {\text{Required}}\,{\text{remainder}} = 1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: