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\(Suppose $173\cdot 927\equiv n\pmod{50}$, where $0\le n< 50$. What is the value of $n$?\)

 May 23, 2021
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Suppose \(173 * 927 n \pmod {50}\) where \(0\le n < 50\).
What is the value of \(n\) ?

 

\(\begin{array}{|rcll|} \hline && \mathbf{ 173 * 927\pmod {50}} \\ &\equiv& 160371 \pmod {50} \\ &\equiv& 160350 + 21 \pmod {50} \\ &\equiv& 3201*50 + 21 \pmod {50} \quad | \quad 3201*50 \equiv 0 \mod{50}\\ &\equiv& 0 + 21 \pmod {50} \\ &\equiv& \mathbf{21 \pmod {50}} \\ \hline \end{array}\)

 

n = 21

 

laugh

 May 23, 2021

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