- #1
diredragon
- 323
- 15
Homework Statement
Let ##({a, b, c}, *,+)## be a finite field. Complete the field table for the operations ##*## and ##+##
##\begin{array}{|c|c|c|c|}
\hline * & a & b & c \\
\hline a & ? & ? & ? \\
\hline b & ? & ? & ? \\
\hline c & ? & ? & b \\
\hline
\end{array}##
##\begin{array}{|c|c|c|c|}
\hline + & a & b & c \\
\hline a & a & ? & ? \\
\hline b & a & c & ? \\
\hline c & a & ? & ? \\
\hline
\end{array}##
Homework Equations
3. The Attempt at a Solution [/B]
I figured that since it is a finite field the operation ##+## must be commutative and must have a symmetric table along the main diagonal.
##\begin{array}{|c|c|c|c|}
\hline + & a & b & c \\
\hline a & a & a & a \\
\hline b & a & c & ? \\
\hline c & a & ? & ? \\
\hline
\end{array}##
Now i have to use the information from the first table that ##c*c = b##. I can use that by seeing that ##b+b = c## and than i can say:
##c*c = b##
##b+b = c##
##c*c + c*c = c##
##c*(c+c) = c##
and i can't figure what this tells me. Other than this i don't see a clue in solving this. Could you provide a helpfull clue?
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