# Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x].

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• March 29th 2012, 03:02 AM
fourth
Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x].
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Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x].
• March 29th 2012, 04:08 AM
Sylvia104
Re: Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x]
$\left[f(x)\right]^2=(2x+1)^2=4x^2+4x+1=1$ in $\mathbb Z_4[x].$ So $f(x)$ is its own inverse in $\mathbb Z_4[x].$