Reaminder

Find the remainder when 2202 is divided by 101 .

3 Answers

1
ninepointcircle ·

By Fermat's Theorem
Since (a,p) = 1
a^{p-1}\equiv a \: \textup{mod}\: p

\Rightarrow 2^{100} \equiv 1\: mod \: 101
\Rightarrow 2^{200} \equiv 1^{2} \equiv 1 \: mod \: 101
\Rightarrow 2^{202} \equiv 4 \: mod \: 101

Hence remainder is 4 :)

262
Aditya Bhutra ·

i really didnt understand .

any simpler approach ?

262
Aditya Bhutra ·

hmm.. got it now.
didnt know this theorem .

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