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What is the remainder when 7^{42} is divided by 16?

 Jun 19, 2020
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What is the remainder when \(7^{42}\) is divided by \(16\)?

 

\(\begin{array}{|rcll|} \hline && 7^{42} \pmod{16} \quad | \quad 7^2 \pmod{16} = 1 \\ &\equiv& 7^{2*21} \pmod{16} \\ &\equiv& \left(7^{2}\right)^{21} \pmod{16} \\ &\equiv& \left(1\right)^{21} \pmod{16} \\ &\equiv& \mathbf{1} \pmod{16} \\ \hline \end{array} \)

 

The remainder is \(\mathbf{1}\)

 

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 Jun 19, 2020

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