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# Suppose 173 * 927 nmod50 where 0<= n< 50. What is the value of n ​

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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

May 23, 2021