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Let $a \equiv 1 \pmod{4}$. Find the value of $6a + 5 \pmod{4}$Express your answer as a residue between 0 and the modulus.

Guest Mar 27, 2017
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 #1
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Can you translate your question into ordinary symbols, so that we can understand your question? Most of us can't read LaTex!. Thanks.

Guest Mar 27, 2017
 #2
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Let

\(a \equiv 1 \pmod{4}\).

Find the value of

\(6a + 5 \pmod{4}\)

Express your answer as a residue between 0 and the modulus.

 

\(\begin{array}{|rcll|} \hline && 6a + 5 \pmod{4} \\ &\equiv& 6a + 5 -4 \pmod{4} \\ &\equiv& 6a + 1 \pmod{4} \quad & | \quad a \equiv 1 \pmod{4} \\ &\equiv& 6\cdot 1 + 1 \pmod{4} \\ &\equiv& 7 -1\cdot 4 \pmod{4} \\ &\equiv& 7 -4 \pmod{4} \\ &\equiv& 3 \pmod{4} \\ \hline \end{array}\)

 

The answer is 3.

 

laugh

heureka  Mar 27, 2017

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