Ec numbers congruent to 7 mod 1063
up vote
1
down vote
favorite
A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$. ec numbers are introduced obtained by the concatenation of two consecutive Mersenne numbers (40952047 for example). Ec(7)=12763 and ec(8)=255127 are both congruent to 7 mod 1063. I did not find yet another example of ec(k) and ec(k+1) both congruent to 7 mod 1063. Is there any particolar mathematical reason, can be that ruled out or is it just coincidence?
number-theory
asked Nov 18 at 8:40
paolo galli
223
add a comment |
up vote
1
down vote
favorite
A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$. ec numbers are introduced obtained by the concatenation of two consecutive Mersenne numbers (40952047 for example). Ec(7)=12763 and ec(8)=255127 are both congruent to 7 mod 1063. I did not find yet another example of ec(k) and ec(k+1) both congruent to 7 mod 1063. Is there any particolar mathematical reason, can be that ruled out or is it just coincidence?
number-theory
asked Nov 18 at 8:40
paolo galli
223
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$. ec numbers are introduced obtained by the concatenation of two consecutive Mersenne numbers (40952047 for example). Ec(7)=12763 and ec(8)=255127 are both congruent to 7 mod 1063. I did not find yet another example of ec(k) and ec(k+1) both congruent to 7 mod 1063. Is there any particolar mathematical reason, can be that ruled out or is it just coincidence?
number-theory
asked Nov 18 at 8:40
paolo galli
223
A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$. ec numbers are introduced obtained by the concatenation of two consecutive Mersenne numbers (40952047 for example). Ec(7)=12763 and ec(8)=255127 are both congruent to 7 mod 1063. I did not find yet another example of ec(k) and ec(k+1) both congruent to 7 mod 1063. Is there any particolar mathematical reason, can be that ruled out or is it just coincidence?
number-theory
number-theory
asked Nov 18 at 8:40
paolo galli
223
asked Nov 18 at 8:40
paolo galli
223
asked Nov 18 at 8:40
paolo galli
223
asked Nov 18 at 8:40
paolo galli
223
asked Nov 18 at 8:40
paolo galli
223
223
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
The numbers
$ec(289922)$ and $ec(289923)$ are both congruent to $7$ modulo $1063$
answered Nov 18 at 19:22
Peter
46.3k1039125
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
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
The numbers
$ec(289922)$ and $ec(289923)$ are both congruent to $7$ modulo $1063$
answered Nov 18 at 19:22
Peter
46.3k1039125
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
add a comment |
up vote
1
down vote
The numbers
$ec(289922)$ and $ec(289923)$ are both congruent to $7$ modulo $1063$
answered Nov 18 at 19:22
Peter
46.3k1039125
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
add a comment |
up vote
1
down vote
up vote
1
down vote
The numbers
$ec(289922)$ and $ec(289923)$ are both congruent to $7$ modulo $1063$
answered Nov 18 at 19:22
Peter
46.3k1039125
The numbers
$ec(289922)$ and $ec(289923)$ are both congruent to $7$ modulo $1063$
answered Nov 18 at 19:22
Peter
46.3k1039125
answered Nov 18 at 19:22
Peter
46.3k1039125
answered Nov 18 at 19:22
Peter
46.3k1039125
answered Nov 18 at 19:22
Peter
46.3k1039125
46.3k1039125
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
add a comment |
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$k=2268439$ is the third solution
– Peter
Nov 18 at 19:24
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
$289922=2*144961$. $144961$ is the concatenation of two squares 12^2 and 31^2.
– paolo galli
Nov 19 at 14:20
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
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%2f3003270%2fec-numbers-congruent-to-7-mod-1063%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
