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Math Help - polynomial

  1. #1
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    polynomial

    Let F be a field and let a(x), b(x), and c(x) be polynomials in F[x] with gcd (a(x),b(x))=1 and with a(x)b(x)=c(x)^n for some n>1. Prove: n=2, a(x)=p₁(x), and b(x)=q₁(x).
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  2. #2
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    Quote Originally Posted by apple2009 View Post
    Let F be a field and let a(x), b(x), and c(x) be polynomials in F[x] with gcd (a(x),b(x))=1 and with a(x)b(x)=c(x)^n for some n>1. Prove: n=2, a(x)=p₁(x), and b(x)=q₁(x).
    who said n must be 2? for example put a(x)=x^n, \ b(x)=(x+1)^n, where n is whatever you like. there must be something missing in your problem.
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