Primitive Polynomial (Field Theory) Question
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Let F = GF(q) where q is a power of an odd prime and let α be a
primitive element in F. Show that α^((q−1)/2) = −1.
Hint: Identify α^((q−1)/2) as one of the roots in F of the polynomial x^2 − 1.
Help would be appreciated,
Thanks
abstract-algebra
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
$endgroup$
add a comment |
$begingroup$
Let F = GF(q) where q is a power of an odd prime and let α be a
primitive element in F. Show that α^((q−1)/2) = −1.
Hint: Identify α^((q−1)/2) as one of the roots in F of the polynomial x^2 − 1.
Help would be appreciated,
Thanks
abstract-algebra
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
$endgroup$
$begingroup$
What is the square of $b=a^{(q-1)/2}$? Can we have $b=1$?
$endgroup$
– Mindlack
Dec 13 '18 at 16:41
add a comment |
$begingroup$
Let F = GF(q) where q is a power of an odd prime and let α be a
primitive element in F. Show that α^((q−1)/2) = −1.
Hint: Identify α^((q−1)/2) as one of the roots in F of the polynomial x^2 − 1.
Help would be appreciated,
Thanks
abstract-algebra
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
$endgroup$
Let F = GF(q) where q is a power of an odd prime and let α be a
primitive element in F. Show that α^((q−1)/2) = −1.
Hint: Identify α^((q−1)/2) as one of the roots in F of the polynomial x^2 − 1.
Help would be appreciated,
Thanks
abstract-algebra
abstract-algebra
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
asked Dec 13 '18 at 15:49
Sharon MishayevSharon Mishayev
1
1
$begingroup$
What is the square of $b=a^{(q-1)/2}$? Can we have $b=1$?
$endgroup$
– Mindlack
Dec 13 '18 at 16:41
add a comment |
$begingroup$
What is the square of $b=a^{(q-1)/2}$? Can we have $b=1$?
$endgroup$
– Mindlack
Dec 13 '18 at 16:41
$begingroup$
What is the square of $b=a^{(q-1)/2}$? Can we have $b=1$?
$endgroup$
– Mindlack
Dec 13 '18 at 16:41
$begingroup$
What is the square of $b=a^{(q-1)/2}$? Can we have $b=1$?
$endgroup$
– Mindlack
Dec 13 '18 at 16:41
add a comment |
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$begingroup$
What is the square of $b=a^{(q-1)/2}$? Can we have $b=1$?
$endgroup$
– Mindlack
Dec 13 '18 at 16:41