Finding a congruence chain (linear and quadratic) equivalent to a polynomial
0
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I want to find a congruence chain (linear and quadratic) equivalent to $2x^2+3x-k equiv 0 (mod5)$, with $k in mathbb{Z}$. I've started with considering the polynomial for $x=1,2,3,4$ but I don't know how one can find a congruence chain.
Can someone explain me what it means?
Thanks
elementary-number-theory modular-arithmetic finite-fields
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
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add a comment |
0
$begingroup$
I want to find a congruence chain (linear and quadratic) equivalent to $2x^2+3x-k equiv 0 (mod5)$, with $k in mathbb{Z}$. I've started with considering the polynomial for $x=1,2,3,4$ but I don't know how one can find a congruence chain.
Can someone explain me what it means?
Thanks
elementary-number-theory modular-arithmetic finite-fields
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
$endgroup$
1
$begingroup$
What is a congruence chain? I don't recall hearing of such a thing. Ok, I do call things like $$3^{13}equiv3^{2cdot6+1}equiv(3^6)^2cdot3^1equiv1^2cdot3equiv3pmod7$$ congruence chains (here modulo $7$), but that does not make sense here.
$endgroup$
– Jyrki Lahtonen
Dec 14 '18 at 13:18
$begingroup$
The text of one exercise call it in this way, probably it's what you mean in the comment
$endgroup$
– Alessar
Dec 14 '18 at 13:51
add a comment |
0
0
0
1
$begingroup$
I want to find a congruence chain (linear and quadratic) equivalent to $2x^2+3x-k equiv 0 (mod5)$, with $k in mathbb{Z}$. I've started with considering the polynomial for $x=1,2,3,4$ but I don't know how one can find a congruence chain.
Can someone explain me what it means?
Thanks
elementary-number-theory modular-arithmetic finite-fields
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
$endgroup$
I want to find a congruence chain (linear and quadratic) equivalent to $2x^2+3x-k equiv 0 (mod5)$, with $k in mathbb{Z}$. I've started with considering the polynomial for $x=1,2,3,4$ but I don't know how one can find a congruence chain.
Can someone explain me what it means?
Thanks
elementary-number-theory modular-arithmetic finite-fields
elementary-number-theory modular-arithmetic finite-fields
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
edited Dec 14 '18 at 11:30
Alessar
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
asked Nov 30 '18 at 8:14
AlessarAlessar
20613
20613
1
$begingroup$
What is a congruence chain? I don't recall hearing of such a thing. Ok, I do call things like $$3^{13}equiv3^{2cdot6+1}equiv(3^6)^2cdot3^1equiv1^2cdot3equiv3pmod7$$ congruence chains (here modulo $7$), but that does not make sense here.
$endgroup$
– Jyrki Lahtonen
Dec 14 '18 at 13:18
$begingroup$
The text of one exercise call it in this way, probably it's what you mean in the comment
$endgroup$
– Alessar
Dec 14 '18 at 13:51
add a comment |
1
$begingroup$
What is a congruence chain? I don't recall hearing of such a thing. Ok, I do call things like $$3^{13}equiv3^{2cdot6+1}equiv(3^6)^2cdot3^1equiv1^2cdot3equiv3pmod7$$ congruence chains (here modulo $7$), but that does not make sense here.
$endgroup$
– Jyrki Lahtonen
Dec 14 '18 at 13:18
$begingroup$
The text of one exercise call it in this way, probably it's what you mean in the comment
$endgroup$
– Alessar
Dec 14 '18 at 13:51
1
1
$begingroup$
What is a congruence chain? I don't recall hearing of such a thing. Ok, I do call things like $$3^{13}equiv3^{2cdot6+1}equiv(3^6)^2cdot3^1equiv1^2cdot3equiv3pmod7$$ congruence chains (here modulo $7$), but that does not make sense here.
$endgroup$
– Jyrki Lahtonen
Dec 14 '18 at 13:18
$begingroup$
What is a congruence chain? I don't recall hearing of such a thing. Ok, I do call things like $$3^{13}equiv3^{2cdot6+1}equiv(3^6)^2cdot3^1equiv1^2cdot3equiv3pmod7$$ congruence chains (here modulo $7$), but that does not make sense here.
$endgroup$
– Jyrki Lahtonen
Dec 14 '18 at 13:18
$begingroup$
The text of one exercise call it in this way, probably it's what you mean in the comment
$endgroup$
– Alessar
Dec 14 '18 at 13:51
$begingroup$
The text of one exercise call it in this way, probably it's what you mean in the comment
$endgroup$
– Alessar
Dec 14 '18 at 13:51
add a comment |
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1
$begingroup$
What is a congruence chain? I don't recall hearing of such a thing. Ok, I do call things like $$3^{13}equiv3^{2cdot6+1}equiv(3^6)^2cdot3^1equiv1^2cdot3equiv3pmod7$$ congruence chains (here modulo $7$), but that does not make sense here.
$endgroup$
– Jyrki Lahtonen
Dec 14 '18 at 13:18
$begingroup$
The text of one exercise call it in this way, probably it's what you mean in the comment
$endgroup$
– Alessar
Dec 14 '18 at 13:51