Mixing
Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4)....
This question already has an answer here:
$-1$ is a quadratic residue modulo $p$ if and only if $pequiv 1pmod{4}$
7 answers
Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4).
enter image description here
That’s right?!
number-theory elementary-number-theory
asked Nov 22 '18 at 9:56
NoorNoor
11
marked as duplicate by Jyrki Lahtonen, Servaes, K B Dave, Lord Shark the Unknown, Brahadeesh Nov 23 '18 at 6:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
This question already has an answer here:
$-1$ is a quadratic residue modulo $p$ if and only if $pequiv 1pmod{4}$
7 answers
Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4).
enter image description here
That’s right?!
number-theory elementary-number-theory
asked Nov 22 '18 at 9:56
NoorNoor
11
marked as duplicate by Jyrki Lahtonen, Servaes, K B Dave, Lord Shark the Unknown, Brahadeesh Nov 23 '18 at 6:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
But I didn't know, can you help me with simple prove, thank you.
– Noor
Nov 22 '18 at 9:58
what have you tried? can you show some work you did?
– Arjang
Nov 22 '18 at 10:05
add a comment |
This question already has an answer here:
$-1$ is a quadratic residue modulo $p$ if and only if $pequiv 1pmod{4}$
7 answers
Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4).
enter image description here
That’s right?!
number-theory elementary-number-theory
asked Nov 22 '18 at 9:56
NoorNoor
11
This question already has an answer here:
$-1$ is a quadratic residue modulo $p$ if and only if $pequiv 1pmod{4}$
7 answers
Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4).
enter image description here
That’s right?!
This question already has an answer here:
$-1$ is a quadratic residue modulo $p$ if and only if $pequiv 1pmod{4}$
7 answers
number-theory elementary-number-theory
number-theory elementary-number-theory
asked Nov 22 '18 at 9:56
NoorNoor
11
asked Nov 22 '18 at 9:56
NoorNoor
11
edited Nov 22 '18 at 18:16
Noor
asked Nov 22 '18 at 9:56
NoorNoor
11
asked Nov 22 '18 at 9:56
NoorNoor
11
asked Nov 22 '18 at 9:56
NoorNoor
11
11
marked as duplicate by Jyrki Lahtonen, Servaes, K B Dave, Lord Shark the Unknown, Brahadeesh Nov 23 '18 at 6:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Jyrki Lahtonen, Servaes, K B Dave, Lord Shark the Unknown, Brahadeesh Nov 23 '18 at 6:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
But I didn't know, can you help me with simple prove, thank you.
– Noor
Nov 22 '18 at 9:58
what have you tried? can you show some work you did?
– Arjang
Nov 22 '18 at 10:05
add a comment |
But I didn't know, can you help me with simple prove, thank you.
– Noor
Nov 22 '18 at 9:58
what have you tried? can you show some work you did?
– Arjang
Nov 22 '18 at 10:05
But I didn't know, can you help me with simple prove, thank you.
– Noor
Nov 22 '18 at 9:58
But I didn't know, can you help me with simple prove, thank you.
– Noor
Nov 22 '18 at 9:58
what have you tried? can you show some work you did?
– Arjang
Nov 22 '18 at 10:05
what have you tried? can you show some work you did?
– Arjang
Nov 22 '18 at 10:05
add a comment |
1 Answer
1
active
oldest
votes
If you tried solving it using Euler's criterion, then you are basically looking for an answer to "When is $frac{p-1}2$ even?" That happens exactly when $p-1$ is divisible by $4$, which is to say $pequiv 1pmod4$.
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
The image is it true?!
– Noor
Nov 22 '18 at 18:27
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
If you tried solving it using Euler's criterion, then you are basically looking for an answer to "When is $frac{p-1}2$ even?" That happens exactly when $p-1$ is divisible by $4$, which is to say $pequiv 1pmod4$.
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
The image is it true?!
– Noor
Nov 22 '18 at 18:27
add a comment |
If you tried solving it using Euler's criterion, then you are basically looking for an answer to "When is $frac{p-1}2$ even?" That happens exactly when $p-1$ is divisible by $4$, which is to say $pequiv 1pmod4$.
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
The image is it true?!
– Noor
Nov 22 '18 at 18:27
add a comment |
If you tried solving it using Euler's criterion, then you are basically looking for an answer to "When is $frac{p-1}2$ even?" That happens exactly when $p-1$ is divisible by $4$, which is to say $pequiv 1pmod4$.
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
If you tried solving it using Euler's criterion, then you are basically looking for an answer to "When is $frac{p-1}2$ even?" That happens exactly when $p-1$ is divisible by $4$, which is to say $pequiv 1pmod4$.
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
answered Nov 22 '18 at 10:02
ArthurArthur
111k7107189
111k7107189
The image is it true?!
– Noor
Nov 22 '18 at 18:27
add a comment |
The image is it true?!
– Noor
Nov 22 '18 at 18:27
The image is it true?!
– Noor
Nov 22 '18 at 18:27
The image is it true?!
– Noor
Nov 22 '18 at 18:27
add a comment |
But I didn't know, can you help me with simple prove, thank you.
– Noor
Nov 22 '18 at 9:58
what have you tried? can you show some work you did?
– Arjang
Nov 22 '18 at 10:05