Unformatted text preview: be positive integers with gcd( m,n ) = d . Show that over any ﬁeld the greatest common divisor of x m-1 and x n-1 is x d-1. Hint: Use the Euclidean algorithm. 4. If E and F are subﬁelds of GF ( p k ) with p m and p n elements respectively, use the previous exercise to show that E ∩ F contain p d elements, where d = gcd( m,n )....
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- Spring '11
- Natural number, Greatest common divisor, cyclic group GF