If ,

where and ,

where is a field of number.

for and

show that:

(Giggle)

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- November 25th 2009, 12:24 AMXingyuanCan any one beat this?(Polynomials)
If ,

where and ,

where is a field of number.

for and

show that:

(Giggle) - November 25th 2009, 02:15 AMShanks
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