Modulo Polynomial Division/Examples/Arbitrary Example 3
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Example of Modulo Polynomial Division
Let:
\(\ds \map f x\) | \(=\) | \(\ds x^3 - x^2 - 1\) | ||||||||||||
\(\ds \map g x\) | \(=\) | \(\ds x - 5\) |
Then $\map f x$ divided by $\map g x$ modulo $11$ is:
- $x^2 + 4 x - 2$
Proof
\(\ds \paren {x - 5} \paren {x^2 + 4 x - 2}\) | \(=\) | \(\ds x^3 - x^2 - 22 x + 10\) | ||||||||||||
\(\ds \) | \(\equiv\) | \(\ds x^3 - x^2 - 1\) | \(\ds \pmod {11}\) |
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): division modulo $n$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): division modulo $n$