Gauss Lemma proof：Number Theory
Number Theory
Proof:Seethelastparagraph,andnotethat(p2−1)/8isevenwhenp=±1(mod8)andoddotherwise.Similarlyfor⌊(p+1)/4 ...。其他文章還包含有：「Gauss'slemma(polynomials)」、「abstractalgebra」、「Gauss'sLemma」、「Gauss'slemma(numbertheory)」、「Gauss'lemma.IfRisaUFD」、「Gauss'sLemma(Polynomial)」、「9.GaussLemma」、「Gauss'slemma(Riemanniangeometry)」
查看更多 離開網站
Gauss's lemma (polynomials)
https://en.wikipedia.org
abstract algebra
https://math.stackexchange.com
All versions of Gauss's Lemma lead to the result you are quoting: that primitive polynomials with integer coefficients are irreducible over Z if ...
Gauss's Lemma
https://people.math.wisc.edu
Then f(x) is irreducible in Q[x]. Proof: Suppose not, we will derive a contradiction. Because irreducibility in. Q[x] is unaffected by dividing ...
Gauss's lemma (number theory)
https://en.wikipedia.org
The proof of the nth-power lemma uses the same ideas that were used in the proof of the quadratic lemma. The existence of the integers π(i) and b(i), and their ...
Gauss' lemma. If R is a UFD
https://www.maths.tcd.ie
We want to prove: Gauss' lemma. If R is a UFD, then R[x] is a UFD. We know that if F is a field, then F[x] is a UFD (by Proposition 47, Theorem 48.
Gauss's Lemma (Polynomial)
https://encyclopedia.pub
Proof: Clearly the product f(x).g(x) of two primitive polynomials has integer coefficients. Therefore, if it is not primitive, there must be a ...
9. Gauss Lemma
https://mathweb.ucsd.edu
Now we give a way to prove that polynomials with integer coefficients are irreducible. Lemma 9.14. Let φ: R −→ S be a ring homomorphism. 4 ...
Gauss's lemma (Riemannian geometry)
https://en.wikipedia.org
Gauss' lemma asserts that the image of a sphere of sufficiently small radius in TpM under the exponential map is perpendicular to all geodesics originating at p ...