Talk:Primitive polynomial

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Doesn't Gauss's lemma [1] state that the product of primitive polynomials is primitive? Then how can all primitive polynomials be irreducible? -3mta3 08:37, 20 July 2005 (UTC)

``Because all minimal polynomials are irreducible, all primitive polynomials are also irreducible. Its not correct that all primitive polynomials are irreducible. Consider x^4+4. One can see that (1,4) = 1, so its a primitive polynomial. But, its not irreducible, since: x^4 + 4 = (x^2 - 2x + 2) *(x^2 + 2 x + 2)

This article is utterly confusing, as it defines two (completely different) notions of primitivity, and then deals only with the second. 21:29, 27 May 2006 (UTC)

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