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# help

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

Jun 19, 2020

#1
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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 $$\mathbf{1}$$

Jun 19, 2020