If , where and , where is a field of number. for and show that:
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If gcd (f(x), g(x))=1, then there exist u(x) and v(x) in K[x] such that u(x)f(x)+v(x)g(x)=1, Thus for any integer m>0, u(x^m)f(x^m)+v(x^m)g(x^m)=1 gcd(f(x^m),g(x^m))=1
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