Number theory vs cubing
0
$begingroup$
Solve this diophantide equation
$$4y^3-3=k^2$$
My way was not successful
First see that $k^2$ is odd, so I assumed that $k=2n+1$.
After simplifying I got:
$$y^3=n^2+n+1$$
And I am stuck here again.
Who has a great solution?
number-theory diophantine-equations
edited Dec 29 '18 at 16:12
amWhy
192k28225439
asked Dec 29 '18 at 15:50
HeartHeart
20516
$endgroup$
add a comment |
0
$begingroup$
Solve this diophantide equation
$$4y^3-3=k^2$$
My way was not successful
First see that $k^2$ is odd, so I assumed that $k=2n+1$.
After simplifying I got:
$$y^3=n^2+n+1$$
And I am stuck here again.
Who has a great solution?
number-theory diophantine-equations
edited Dec 29 '18 at 16:12
amWhy
192k28225439
asked Dec 29 '18 at 15:50
HeartHeart
20516
$endgroup$
1
$begingroup$
This is an example of Mordell's equation for an elliptic curve. It has been solved ("great solution") here at this site already. Have a look at this question and related ones (like this one).
$endgroup$
– Dietrich Burde
Dec 29 '18 at 15:56
$begingroup$
By examination of simple instances of your simplification, $y=7, n=18$ is one solution, yielding $k=37$. There may be others.
$endgroup$
– Keith Backman
Dec 29 '18 at 16:47
add a comment |
0
0
0
$begingroup$
Solve this diophantide equation
$$4y^3-3=k^2$$
My way was not successful
First see that $k^2$ is odd, so I assumed that $k=2n+1$.
After simplifying I got:
$$y^3=n^2+n+1$$
And I am stuck here again.
Who has a great solution?
number-theory diophantine-equations
edited Dec 29 '18 at 16:12
amWhy
192k28225439
asked Dec 29 '18 at 15:50
HeartHeart
20516
$endgroup$
Solve this diophantide equation
$$4y^3-3=k^2$$
My way was not successful
First see that $k^2$ is odd, so I assumed that $k=2n+1$.
After simplifying I got:
$$y^3=n^2+n+1$$
And I am stuck here again.
Who has a great solution?
number-theory diophantine-equations
number-theory diophantine-equations
edited Dec 29 '18 at 16:12
amWhy
192k28225439
asked Dec 29 '18 at 15:50
HeartHeart
20516
edited Dec 29 '18 at 16:12
amWhy
192k28225439
asked Dec 29 '18 at 15:50
HeartHeart
20516
edited Dec 29 '18 at 16:12
amWhy
192k28225439
edited Dec 29 '18 at 16:12
amWhy
192k28225439
edited Dec 29 '18 at 16:12
amWhy
192k28225439
192k28225439
asked Dec 29 '18 at 15:50
HeartHeart
20516
asked Dec 29 '18 at 15:50
HeartHeart
20516
asked Dec 29 '18 at 15:50
HeartHeart
20516
20516
1
$begingroup$
This is an example of Mordell's equation for an elliptic curve. It has been solved ("great solution") here at this site already. Have a look at this question and related ones (like this one).
$endgroup$
– Dietrich Burde
Dec 29 '18 at 15:56
$begingroup$
By examination of simple instances of your simplification, $y=7, n=18$ is one solution, yielding $k=37$. There may be others.
$endgroup$
– Keith Backman
Dec 29 '18 at 16:47
add a comment |
1
$begingroup$
This is an example of Mordell's equation for an elliptic curve. It has been solved ("great solution") here at this site already. Have a look at this question and related ones (like this one).
$endgroup$
– Dietrich Burde
Dec 29 '18 at 15:56
$begingroup$
By examination of simple instances of your simplification, $y=7, n=18$ is one solution, yielding $k=37$. There may be others.
$endgroup$
– Keith Backman
Dec 29 '18 at 16:47
1
1
$begingroup$
This is an example of Mordell's equation for an elliptic curve. It has been solved ("great solution") here at this site already. Have a look at this question and related ones (like this one).
$endgroup$
– Dietrich Burde
Dec 29 '18 at 15:56
$begingroup$
This is an example of Mordell's equation for an elliptic curve. It has been solved ("great solution") here at this site already. Have a look at this question and related ones (like this one).
$endgroup$
– Dietrich Burde
Dec 29 '18 at 15:56
$begingroup$
By examination of simple instances of your simplification, $y=7, n=18$ is one solution, yielding $k=37$. There may be others.
$endgroup$
– Keith Backman
Dec 29 '18 at 16:47
$begingroup$
By examination of simple instances of your simplification, $y=7, n=18$ is one solution, yielding $k=37$. There may be others.
$endgroup$
– Keith Backman
Dec 29 '18 at 16:47
add a comment |
0
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1
$begingroup$
This is an example of Mordell's equation for an elliptic curve. It has been solved ("great solution") here at this site already. Have a look at this question and related ones (like this one).
$endgroup$
– Dietrich Burde
Dec 29 '18 at 15:56
$begingroup$
By examination of simple instances of your simplification, $y=7, n=18$ is one solution, yielding $k=37$. There may be others.
$endgroup$
– Keith Backman
Dec 29 '18 at 16:47