Existence of a constant for every prime
up vote
3
down vote
favorite
Prove the existence of a constant $c$$>0$,such that for every prime
number there are at most $cp^{2/3}$ positive integers $n$,for which
$n!$$+1$ is divisible by $p$.
If, for every prime $p$, the set of integers with the property is {${a_1,...,a_k}$} we have that there are at most $s$ differences between $a_i$ and $a_j$ equal to $s$, but I can't continue.
number-theory prime-numbers
edited Nov 21 at 11:46
Flermat
1,28311129
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
add a comment |
up vote
3
down vote
favorite
Prove the existence of a constant $c$$>0$,such that for every prime
number there are at most $cp^{2/3}$ positive integers $n$,for which
$n!$$+1$ is divisible by $p$.
If, for every prime $p$, the set of integers with the property is {${a_1,...,a_k}$} we have that there are at most $s$ differences between $a_i$ and $a_j$ equal to $s$, but I can't continue.
number-theory prime-numbers
edited Nov 21 at 11:46
Flermat
1,28311129
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
This is not an original problem,I found it in Problems from the Book.
– Kristiyan Vasilev
Feb 18 '17 at 17:54
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Prove the existence of a constant $c$$>0$,such that for every prime
number there are at most $cp^{2/3}$ positive integers $n$,for which
$n!$$+1$ is divisible by $p$.
If, for every prime $p$, the set of integers with the property is {${a_1,...,a_k}$} we have that there are at most $s$ differences between $a_i$ and $a_j$ equal to $s$, but I can't continue.
number-theory prime-numbers
edited Nov 21 at 11:46
Flermat
1,28311129
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
Prove the existence of a constant $c$$>0$,such that for every prime
number there are at most $cp^{2/3}$ positive integers $n$,for which
$n!$$+1$ is divisible by $p$.
If, for every prime $p$, the set of integers with the property is {${a_1,...,a_k}$} we have that there are at most $s$ differences between $a_i$ and $a_j$ equal to $s$, but I can't continue.
number-theory prime-numbers
number-theory prime-numbers
edited Nov 21 at 11:46
Flermat
1,28311129
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
edited Nov 21 at 11:46
Flermat
1,28311129
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
edited Nov 21 at 11:46
Flermat
1,28311129
edited Nov 21 at 11:46
Flermat
1,28311129
edited Nov 21 at 11:46
Flermat
1,28311129
1,28311129
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
asked Feb 18 '17 at 17:53
Kristiyan Vasilev
1255
1255
This is not an original problem,I found it in Problems from the Book.
– Kristiyan Vasilev
Feb 18 '17 at 17:54
add a comment |
This is not an original problem,I found it in Problems from the Book.
– Kristiyan Vasilev
Feb 18 '17 at 17:54
This is not an original problem,I found it in Problems from the Book.
– Kristiyan Vasilev
Feb 18 '17 at 17:54
This is not an original problem,I found it in Problems from the Book.
– Kristiyan Vasilev
Feb 18 '17 at 17:54
add a comment |
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2150347%2fexistence-of-a-constant-for-every-prime%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
This is not an original problem,I found it in Problems from the Book.
– Kristiyan Vasilev
Feb 18 '17 at 17:54