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Results tagged with hyperelliptic-curves
Search options questions only
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user 12481
-1
votes
1
answer
312
views
Bounds for the number of points on projective hyperelliptic curves over finite fields
Let $C$ be projective hyperelliptic curve over finite field $K$.
What are bounds for the number of points $\#C(K)$?
The Hasse-Weil bound requires smooth curves, and hyperelliptic curves are
not smooth …
- 25.4k
0
votes
0
answers
94
views
Elementary constraints for the solutions of $z^{n-2}y(y+z)=x^n$?
Related to FLT and this question.
For natural $n > 4 $ define the curve $C_n : z^{n-2}y(y+z)=x^n$.
$C_n$ has the trivial points with $x=0$ for all $n$.
The answer in the linked question shows there …
- 25.4k
7
votes
1
answer
313
views
Rational perfect power values of $y(y+1)$
This is hard, so I am looking for partial results and how hard it is.
Let $n>4$. Is it true that the hyperelliptic curve $x^n=y(y+1)$
doesn't have rational point with $x \ne 0$?
If necessarily assum …
- 25.4k
1
vote
2
answers
351
views
Hyperelliptic curves imply FLT-like results
Probably this is known, but doesn't show in searches.
If a certain hyperelliptic curve has only trivial rational points,
FLT-like curve also has only trivial rationals points for fixed $n$.
Working …
- 30.5k
5
votes
0
answers
233
views
No rational points on $x^n+a=y^2$ for all $n>4$"?
Is there rational (or better integer) $a$ such that for all $n>4$,$x^n+a=y^2$
has no rational points?
- 4,746