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MATH / Recall that if b is a residue pmod{m}, then the modular inverse of b is the residue c for which bc equiv 1pmod{m}. The table below shows the inverses of the first 9 positive residu…

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Recall that if bb is a residue $\pmod{m}$, then the modular inverse of bb is the residue cc for which $bc \equiv 1\pmod{m}$. The table below shows the inverses of the first 9 positive residues modulo 47. \begin{tabular}{c|ccccccccc} bb & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline inverse of b\,b & 1 & 24 & 16 & 12 & 19 & 8 & 27 & 6 & 21 \end{tabular}Find the modular inverse of $35\pmod{47}$. Express your answer as an integer from 00 to 4646, inclusive.
Plain-text mathematical notation (without MathML)
Recall that if b is a residue $\pmod{m}$, then the modular inverse of b is the residue c for which $bc \equiv 1\pmod{m}$. The table below shows the inverses of the first 9 positive residues modulo 47.  \begin{tabular}{c|ccccccccc}
b & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
inverse of  b & 1 & 24 & 16 & 12 & 19 & 8 & 27 & 6 & 21
\end{tabular}Find the modular inverse of $35\pmod{47}$.

Express your answer as an integer from 0 to 46, inclusive.
Original LaTeX notation
Recall that if $b$ is a residue $\pmod{m}$, then the modular inverse of $b$ is the residue $c$ for which $bc \equiv 1\pmod{m}$. The table below shows the inverses of the first 9 positive residues modulo 47.  \begin{tabular}{c|ccccccccc}
$b$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
inverse of $\,b$ & 1 & 24 & 16 & 12 & 19 & 8 & 27 & 6 & 21
\end{tabular}Find the modular inverse of $35\pmod{47}$.

Express your answer as an integer from $0$ to $46$, inclusive.

level

Level 4

type

Number Theory

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task_id
14d9f0f1-be0d-5472-990b-359c84cddb00
task_key
number~5ftheory--test--14d9f0f1-be0d-5472-990b-359c84cddb00
task_revision_id
1
config / split
number_theory / test

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