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Math Help - congruent mod

  1. #1
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    omaha
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    congruent mod

    Determine whether or not x3 +2x+1 and x4 +3x-2 are congruent mod
    x2 + 2x + 2 in Q[x]. Answer the same question for x4 + x3 + x2 + 2 and x3 + 1
    mod(x2 + 1) in Z3[x].

    Help please.
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: congruent mod

    If you learn latex, then you will get answers a lot quicker. A quick search on google should get you started along with [*tex][*/tex] boxes. I'm assuming by Q[x] you mean rational numbers, but I don't know what you mean by "Z3[x]" In your own words, explain what it means

    We are asked whether or not x^3+2x+1 \equiv x^4+3x-2 \mod{x^2+2x+2} is true in the space of rational numbers.

    If this were true then x^2+2x+2 divides the difference (x^4+3x-2) - (x^2+2x+1) = x^4-x^2+x-3 with a rational quotient and no remainder.
    Use polynomial long division to verify whether or not it is the case.

    If I'm missing something, let me know.
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