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

  1. March 29th 2012, 03:02 AM #1
    fourth
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    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].
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  2. March 29th 2012, 04:08 AM #2
    Sylvia104
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    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].
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