A question about zeroes in Fp
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I' m thinking a question.
Is it true the following proposition:
Fixed a polynomial $f(x) in mathbbZ[x]$, there exists always a prime $p$ such that $ f(x)$ splits completely in $mathbbF_p[x]$ ?
elementary-number-theory polynomials
asked Sep 8 at 12:12
Matvey Tizovsky
242
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up vote
1
down vote
favorite
1
I' m thinking a question.
Is it true the following proposition:
Fixed a polynomial $f(x) in mathbbZ[x]$, there exists always a prime $p$ such that $ f(x)$ splits completely in $mathbbF_p[x]$ ?
elementary-number-theory polynomials
asked Sep 8 at 12:12
Matvey Tizovsky
242
1
Check out the Chebotarev Density Theorem, and report back on your findings.
– Gerry Myerson
Sep 8 at 13:10
1
I find an article by Lenstra about the frobenius theorem and the relation between the automorphism in the Galois group and the "splitting type" of the polynomial mod p. The proposition is true because there is always the identity element. But is there a more direct approach to solve the question?
– Matvey Tizovsky
Sep 8 at 14:54
add a comment |Â
up vote
1
down vote
favorite
1
up vote
1
down vote
favorite
1
1
I' m thinking a question.
Is it true the following proposition:
Fixed a polynomial $f(x) in mathbbZ[x]$, there exists always a prime $p$ such that $ f(x)$ splits completely in $mathbbF_p[x]$ ?
elementary-number-theory polynomials
asked Sep 8 at 12:12
Matvey Tizovsky
242
I' m thinking a question.
Is it true the following proposition:
Fixed a polynomial $f(x) in mathbbZ[x]$, there exists always a prime $p$ such that $ f(x)$ splits completely in $mathbbF_p[x]$ ?
elementary-number-theory polynomials
elementary-number-theory polynomials
asked Sep 8 at 12:12
Matvey Tizovsky
242
asked Sep 8 at 12:12
Matvey Tizovsky
242
asked Sep 8 at 12:12
Matvey Tizovsky
242
asked Sep 8 at 12:12
Matvey Tizovsky
242
asked Sep 8 at 12:12
Matvey Tizovsky
242
242
1
Check out the Chebotarev Density Theorem, and report back on your findings.
– Gerry Myerson
Sep 8 at 13:10
1
I find an article by Lenstra about the frobenius theorem and the relation between the automorphism in the Galois group and the "splitting type" of the polynomial mod p. The proposition is true because there is always the identity element. But is there a more direct approach to solve the question?
– Matvey Tizovsky
Sep 8 at 14:54
add a comment |Â
1
Check out the Chebotarev Density Theorem, and report back on your findings.
– Gerry Myerson
Sep 8 at 13:10
1
I find an article by Lenstra about the frobenius theorem and the relation between the automorphism in the Galois group and the "splitting type" of the polynomial mod p. The proposition is true because there is always the identity element. But is there a more direct approach to solve the question?
– Matvey Tizovsky
Sep 8 at 14:54
1
1
Check out the Chebotarev Density Theorem, and report back on your findings.
– Gerry Myerson
Sep 8 at 13:10
Check out the Chebotarev Density Theorem, and report back on your findings.
– Gerry Myerson
Sep 8 at 13:10
1
1
I find an article by Lenstra about the frobenius theorem and the relation between the automorphism in the Galois group and the "splitting type" of the polynomial mod p. The proposition is true because there is always the identity element. But is there a more direct approach to solve the question?
– Matvey Tizovsky
Sep 8 at 14:54
I find an article by Lenstra about the frobenius theorem and the relation between the automorphism in the Galois group and the "splitting type" of the polynomial mod p. The proposition is true because there is always the identity element. But is there a more direct approach to solve the question?
– Matvey Tizovsky
Sep 8 at 14:54
add a comment |Â
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1
Check out the Chebotarev Density Theorem, and report back on your findings.
– Gerry Myerson
Sep 8 at 13:10
1
I find an article by Lenstra about the frobenius theorem and the relation between the automorphism in the Galois group and the "splitting type" of the polynomial mod p. The proposition is true because there is always the identity element. But is there a more direct approach to solve the question?
– Matvey Tizovsky
Sep 8 at 14:54