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The property of being Landweber exact is independent of the orientation. In terms of Landweber's criterion, this is generally phrased as saying that the element v_n is invariant modulo the ideal (p,v₁,...,v_n-1), and so any change-of-orientation (which induces a strict isomorphism on the formal group law) does not change the property of v_n being or not being a zero divisor after modding out the previous terms.