Name of the theorem used for testing the primality of a number
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$n$ is prime $iff$ $a^{n-1} equiv 1 mod n hspace{10mm} forall 1 le a le n-1$
What is the name of this theorem in literature?
elementary-number-theory reference-request prime-numbers primality-test
asked Nov 22 at 7:50
hanugm
817621
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up vote
-1
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favorite
$n$ is prime $iff$ $a^{n-1} equiv 1 mod n hspace{10mm} forall 1 le a le n-1$
What is the name of this theorem in literature?
elementary-number-theory reference-request prime-numbers primality-test
asked Nov 22 at 7:50
hanugm
817621
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
$n$ is prime $iff$ $a^{n-1} equiv 1 mod n hspace{10mm} forall 1 le a le n-1$
What is the name of this theorem in literature?
elementary-number-theory reference-request prime-numbers primality-test
asked Nov 22 at 7:50
hanugm
817621
$n$ is prime $iff$ $a^{n-1} equiv 1 mod n hspace{10mm} forall 1 le a le n-1$
What is the name of this theorem in literature?
elementary-number-theory reference-request prime-numbers primality-test
elementary-number-theory reference-request prime-numbers primality-test
asked Nov 22 at 7:50
hanugm
817621
asked Nov 22 at 7:50
hanugm
817621
edited Nov 22 at 8:01
asked Nov 22 at 7:50
hanugm
817621
asked Nov 22 at 7:50
hanugm
817621
asked Nov 22 at 7:50
hanugm
817621
817621
add a comment |
add a comment |
1 Answer
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1
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$Longrightarrow$ is Fermat's little theorem
$Longleftarrow$ is the definition of prime: any $a<n$ is coprime to $n$, and therefore $n$ must be prime.
answered Nov 22 at 8:02
Arthur
108k7103186
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
$Longrightarrow$ is Fermat's little theorem
$Longleftarrow$ is the definition of prime: any $a<n$ is coprime to $n$, and therefore $n$ must be prime.
answered Nov 22 at 8:02
Arthur
108k7103186
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
add a comment |
up vote
1
down vote
$Longrightarrow$ is Fermat's little theorem
$Longleftarrow$ is the definition of prime: any $a<n$ is coprime to $n$, and therefore $n$ must be prime.
answered Nov 22 at 8:02
Arthur
108k7103186
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
add a comment |
up vote
1
down vote
up vote
1
down vote
$Longrightarrow$ is Fermat's little theorem
$Longleftarrow$ is the definition of prime: any $a<n$ is coprime to $n$, and therefore $n$ must be prime.
answered Nov 22 at 8:02
Arthur
108k7103186
$Longrightarrow$ is Fermat's little theorem
$Longleftarrow$ is the definition of prime: any $a<n$ is coprime to $n$, and therefore $n$ must be prime.
answered Nov 22 at 8:02
Arthur
108k7103186
answered Nov 22 at 8:02
Arthur
108k7103186
answered Nov 22 at 8:02
Arthur
108k7103186
answered Nov 22 at 8:02
Arthur
108k7103186
108k7103186
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
add a comment |
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
Does the prime definition have any other name?
– hanugm
Nov 22 at 8:06
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
@hanugm Why would you want another name?
– Arthur
Nov 22 at 8:09
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
$implies$ part is fine but does the other part has any other name other than saying as a prime definition? Because it is a key property for prime numbers, so I am guessing that some name should be there for that result.
– hanugm
Nov 22 at 8:11
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
I want to see for its complete reference, so the name of the theorem would help me a lot.
– hanugm
Nov 22 at 8:12
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
@hanugm It's such an immediate consequence of the definition of prime numbers, yet it's relatively specialised. I can't imagine that it has a name. Call the entire thing "Fermat's little theorem", and no one would bat an eye.
– Arthur
Nov 22 at 8:16
add a comment |
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