Legendre (p/q) = 1 what can we conclude about the solution of $n^2 equiv p$ mod q? [on hold]
Let p and q be odd primes and Legendre (p/q)=1. So we know that there exists (at least) one whole number n for which $n^2 equiv p$ mod q holds.
Is it possible to deduce that there must be an odd n from these facts, without having a solution procedure for $n^2 equiv p$ mod q, where we can possibly see wether even and/or odd solutions occur.
I've calculated some examples, so I'v seen there might be always two solutions, one n even, one n odd.
Please for now only yes or no as answer and perhaps a little hint.
Thank you.
modular-arithmetic
asked Dec 26 at 8:06
i-have-no-clue
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, Lord Shark the Unknown, Saad, Lord_Farin, Cesareo Dec 26 at 10:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Saad, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Let p and q be odd primes and Legendre (p/q)=1. So we know that there exists (at least) one whole number n for which $n^2 equiv p$ mod q holds.
Is it possible to deduce that there must be an odd n from these facts, without having a solution procedure for $n^2 equiv p$ mod q, where we can possibly see wether even and/or odd solutions occur.
I've calculated some examples, so I'v seen there might be always two solutions, one n even, one n odd.
Please for now only yes or no as answer and perhaps a little hint.
Thank you.
modular-arithmetic
asked Dec 26 at 8:06
i-have-no-clue
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, Lord Shark the Unknown, Saad, Lord_Farin, Cesareo Dec 26 at 10:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Saad, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
$n^2equiv ppmod qRightarrow (n+q)^2equiv ppmod q$
– Minz
Dec 26 at 9:22
add a comment |
Let p and q be odd primes and Legendre (p/q)=1. So we know that there exists (at least) one whole number n for which $n^2 equiv p$ mod q holds.
Is it possible to deduce that there must be an odd n from these facts, without having a solution procedure for $n^2 equiv p$ mod q, where we can possibly see wether even and/or odd solutions occur.
I've calculated some examples, so I'v seen there might be always two solutions, one n even, one n odd.
Please for now only yes or no as answer and perhaps a little hint.
Thank you.
modular-arithmetic
asked Dec 26 at 8:06
i-have-no-clue
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let p and q be odd primes and Legendre (p/q)=1. So we know that there exists (at least) one whole number n for which $n^2 equiv p$ mod q holds.
Is it possible to deduce that there must be an odd n from these facts, without having a solution procedure for $n^2 equiv p$ mod q, where we can possibly see wether even and/or odd solutions occur.
I've calculated some examples, so I'v seen there might be always two solutions, one n even, one n odd.
Please for now only yes or no as answer and perhaps a little hint.
Thank you.
modular-arithmetic
modular-arithmetic
asked Dec 26 at 8:06
i-have-no-clue
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 8:06
i-have-no-clue
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Dec 26 at 8:54
asked Dec 26 at 8:06
i-have-no-clue
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 8:06
i-have-no-clue
11
asked Dec 26 at 8:06
i-have-no-clue
11
11
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
i-have-no-clue is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, Lord Shark the Unknown, Saad, Lord_Farin, Cesareo Dec 26 at 10:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Saad, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Eevee Trainer, Lord Shark the Unknown, Saad, Lord_Farin, Cesareo Dec 26 at 10:24
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Saad, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
$n^2equiv ppmod qRightarrow (n+q)^2equiv ppmod q$
– Minz
Dec 26 at 9:22
add a comment |
$n^2equiv ppmod qRightarrow (n+q)^2equiv ppmod q$
– Minz
Dec 26 at 9:22
$n^2equiv ppmod qRightarrow (n+q)^2equiv ppmod q$
– Minz
Dec 26 at 9:22
$n^2equiv ppmod qRightarrow (n+q)^2equiv ppmod q$
– Minz
Dec 26 at 9:22
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
$n^2equiv ppmod qRightarrow (n+q)^2equiv ppmod q$
– Minz
Dec 26 at 9:22