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\(Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. (Give a number between 0 and 46, inclusive.)\)

 May 27, 2020
 #1
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Fix ur latex bro

 May 28, 2020
 #2
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help please

\(\text{Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. $\\$(Give a number between 0 and 46, inclusive.)}\)

 

\(\begin{array}{|rcll|} \hline &&\mathbf{ 34^{-1} \pmod{47} } \\ &\equiv& (34-47)^{-1} \pmod{47} \\ &\equiv& (-13)^{-1} \pmod{47} \\ &\equiv& -(13)^{-1} \pmod{47} \quad | \quad 13^{-1}\pmod{47} = 29 \\ &\equiv& -29 \pmod{47} \\ &\equiv& -29+47 \pmod{47} \\ &\equiv& \mathbf{18 \pmod{47} } \\ \hline \end{array}\)

 

laugh

 May 28, 2020

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