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Results tagged with abelian-varieties
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user 134689
Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.
2
votes
Relation between elliptic curve and Fermat's last thereom
In 1969 Hellegouarch performed the elliptic curves $F (a, b)$, which were later named after Gerhard Frey and were constructed from the solutions of the Fermat equation, he reported on the curves in a …
-4
votes
3
answers
498
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Relation between elliptic curve and Fermat's last thereom
I am looking for a elaborate explanation how the elliptic curve $E (a, b) := y^2=x(x-a)(x-b)$ is associated with the solution of $a^n+b^n=c^n$.
In 1969 Hellegouarch performed the elliptic curves $E (a …
1
vote
0
answers
191
views
Integer solutions of Diophantine equation $y^2= 1+4n^{\underline k} $
I am looking for the integer solutions for the diophantine equation $y^2 =4n(n-1)(n-2)\cdots (n-k+1)+1$ for a given $k$ where $n>k+1>5$.
In other words,
$$y^2=1+4n^{\underline k},\tag{I}$$
where $n^{\ …