How to prove the mersenne number is not pseudoprimes to the base 3?
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
i start think to take a small factor $p$ of $M_n$ after supposing $M_n$ is composite, then i reached that $ord_p(3)mid M_n-1$
Now how i can continue to reached that $p$ is the same as $M_n$ ??
abstract-algebra number-theory primality-test research pseudoprimes
asked Aug 19 at 4:06
Ramez Hindi
1346
add a comment |Â
up vote
0
down vote
favorite
i start think to take a small factor $p$ of $M_n$ after supposing $M_n$ is composite, then i reached that $ord_p(3)mid M_n-1$
Now how i can continue to reached that $p$ is the same as $M_n$ ??
abstract-algebra number-theory primality-test research pseudoprimes
asked Aug 19 at 4:06
Ramez Hindi
1346
I think it is quite difficult to prove that a composite Mersenne-number is never a $3$-weak-Fermat-pseudoprime. I am not aware of useful conditions to rule this and similar things out.
– Peter
Aug 19 at 11:35
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
i start think to take a small factor $p$ of $M_n$ after supposing $M_n$ is composite, then i reached that $ord_p(3)mid M_n-1$
Now how i can continue to reached that $p$ is the same as $M_n$ ??
abstract-algebra number-theory primality-test research pseudoprimes
asked Aug 19 at 4:06
Ramez Hindi
1346
i start think to take a small factor $p$ of $M_n$ after supposing $M_n$ is composite, then i reached that $ord_p(3)mid M_n-1$
Now how i can continue to reached that $p$ is the same as $M_n$ ??
abstract-algebra number-theory primality-test research pseudoprimes
asked Aug 19 at 4:06
Ramez Hindi
1346
asked Aug 19 at 4:06
Ramez Hindi
1346
asked Aug 19 at 4:06
Ramez Hindi
1346
asked Aug 19 at 4:06
Ramez Hindi
1346
1346
I think it is quite difficult to prove that a composite Mersenne-number is never a $3$-weak-Fermat-pseudoprime. I am not aware of useful conditions to rule this and similar things out.
– Peter
Aug 19 at 11:35
add a comment |Â
I think it is quite difficult to prove that a composite Mersenne-number is never a $3$-weak-Fermat-pseudoprime. I am not aware of useful conditions to rule this and similar things out.
– Peter
Aug 19 at 11:35
I think it is quite difficult to prove that a composite Mersenne-number is never a $3$-weak-Fermat-pseudoprime. I am not aware of useful conditions to rule this and similar things out.
– Peter
Aug 19 at 11:35
I think it is quite difficult to prove that a composite Mersenne-number is never a $3$-weak-Fermat-pseudoprime. I am not aware of useful conditions to rule this and similar things out.
– Peter
Aug 19 at 11:35
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2887340%2fhow-to-prove-the-mersenne-number-is-not-pseudoprimes-to-the-base-3%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
I think it is quite difficult to prove that a composite Mersenne-number is never a $3$-weak-Fermat-pseudoprime. I am not aware of useful conditions to rule this and similar things out.
– Peter
Aug 19 at 11:35