Trivial solutions of a diophantine equation
Let $K$ be an odd degree number field. Consider the Diophantine equation:
$$
X^4 + bY^4 =Z^2
$$
where $bneq 0$.
Say we know that the above equation has only trivial roots in $K$ (for some fixed value of $b$). If $din Ksetminus K^2$, when does $X^4 + d^2b Y^4=Z^2$ have only trivial roots in $K$?
number-theory diophantine-equations elliptic-curves
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
add a comment |
Let $K$ be an odd degree number field. Consider the Diophantine equation:
$$
X^4 + bY^4 =Z^2
$$
where $bneq 0$.
Say we know that the above equation has only trivial roots in $K$ (for some fixed value of $b$). If $din Ksetminus K^2$, when does $X^4 + d^2b Y^4=Z^2$ have only trivial roots in $K$?
number-theory diophantine-equations elliptic-curves
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
3
Cross-posted: mathoverflow.net/questions/316812
– Watson
Dec 3 '18 at 17:03
add a comment |
Let $K$ be an odd degree number field. Consider the Diophantine equation:
$$
X^4 + bY^4 =Z^2
$$
where $bneq 0$.
Say we know that the above equation has only trivial roots in $K$ (for some fixed value of $b$). If $din Ksetminus K^2$, when does $X^4 + d^2b Y^4=Z^2$ have only trivial roots in $K$?
number-theory diophantine-equations elliptic-curves
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
Let $K$ be an odd degree number field. Consider the Diophantine equation:
$$
X^4 + bY^4 =Z^2
$$
where $bneq 0$.
Say we know that the above equation has only trivial roots in $K$ (for some fixed value of $b$). If $din Ksetminus K^2$, when does $X^4 + d^2b Y^4=Z^2$ have only trivial roots in $K$?
number-theory diophantine-equations elliptic-curves
number-theory diophantine-equations elliptic-curves
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
asked Dec 3 '18 at 15:17
debanjanadebanjana
387111
387111
3
Cross-posted: mathoverflow.net/questions/316812
– Watson
Dec 3 '18 at 17:03
add a comment |
3
Cross-posted: mathoverflow.net/questions/316812
– Watson
Dec 3 '18 at 17:03
3
3
Cross-posted: mathoverflow.net/questions/316812
– Watson
Dec 3 '18 at 17:03
Cross-posted: mathoverflow.net/questions/316812
– Watson
Dec 3 '18 at 17:03
add a comment |
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3
Cross-posted: mathoverflow.net/questions/316812
– Watson
Dec 3 '18 at 17:03