Other diophantine equations solved thanks to modularity theorem
up vote
2
down vote
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The diophantine equation
begin{equation}
x^n+y^n=z^n
end{equation}
is an example of an equation that was not solved before the work of Wiles, and has now been solved through his and other's recent methods. What are other Diophantine equations that were not solved before 1994 and now are, thanks to the modularity theorem?
number-theory reference-request diophantine-equations
asked Jul 13 at 8:19
Marco Flores
1,741826
add a comment |
up vote
2
down vote
favorite
The diophantine equation
begin{equation}
x^n+y^n=z^n
end{equation}
is an example of an equation that was not solved before the work of Wiles, and has now been solved through his and other's recent methods. What are other Diophantine equations that were not solved before 1994 and now are, thanks to the modularity theorem?
number-theory reference-request diophantine-equations
asked Jul 13 at 8:19
Marco Flores
1,741826
1
I wonder .. could we say the equation was "solved"? It was proved that there are no integer solutions (n>2), but on the other hand really it is some kind of negative solution..
– Widawensen
Jul 13 at 10:56
Beal's conjecture and the Fermat-Catalan-conjecture are obvious generalizations of Fermat's last theorem, but they are both unsolved.
– Peter
Jul 13 at 19:30
There is Denes' conjecture (Ribet), and FLT over $Bbb Q(sqrt 2)$ (Jarvis and Meekin). See also here and this paper.
– Watson
Aug 28 at 12:41
See also this question: math.stackexchange.com/questions/1466539
– Watson
Aug 28 at 12:47
@Widawensen to me "solving" means presenting with proof the set of solutions (: And the empty set is a set
– Marco Flores
Nov 19 at 12:14
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
The diophantine equation
begin{equation}
x^n+y^n=z^n
end{equation}
is an example of an equation that was not solved before the work of Wiles, and has now been solved through his and other's recent methods. What are other Diophantine equations that were not solved before 1994 and now are, thanks to the modularity theorem?
number-theory reference-request diophantine-equations
asked Jul 13 at 8:19
Marco Flores
1,741826
The diophantine equation
begin{equation}
x^n+y^n=z^n
end{equation}
is an example of an equation that was not solved before the work of Wiles, and has now been solved through his and other's recent methods. What are other Diophantine equations that were not solved before 1994 and now are, thanks to the modularity theorem?
number-theory reference-request diophantine-equations
number-theory reference-request diophantine-equations
asked Jul 13 at 8:19
Marco Flores
1,741826
asked Jul 13 at 8:19
Marco Flores
1,741826
edited Jul 13 at 10:01
asked Jul 13 at 8:19
Marco Flores
1,741826
asked Jul 13 at 8:19
Marco Flores
1,741826
asked Jul 13 at 8:19
Marco Flores
1,741826
1,741826
1
I wonder .. could we say the equation was "solved"? It was proved that there are no integer solutions (n>2), but on the other hand really it is some kind of negative solution..
– Widawensen
Jul 13 at 10:56
Beal's conjecture and the Fermat-Catalan-conjecture are obvious generalizations of Fermat's last theorem, but they are both unsolved.
– Peter
Jul 13 at 19:30
There is Denes' conjecture (Ribet), and FLT over $Bbb Q(sqrt 2)$ (Jarvis and Meekin). See also here and this paper.
– Watson
Aug 28 at 12:41
See also this question: math.stackexchange.com/questions/1466539
– Watson
Aug 28 at 12:47
@Widawensen to me "solving" means presenting with proof the set of solutions (: And the empty set is a set
– Marco Flores
Nov 19 at 12:14
add a comment |
1
I wonder .. could we say the equation was "solved"? It was proved that there are no integer solutions (n>2), but on the other hand really it is some kind of negative solution..
– Widawensen
Jul 13 at 10:56
Beal's conjecture and the Fermat-Catalan-conjecture are obvious generalizations of Fermat's last theorem, but they are both unsolved.
– Peter
Jul 13 at 19:30
There is Denes' conjecture (Ribet), and FLT over $Bbb Q(sqrt 2)$ (Jarvis and Meekin). See also here and this paper.
– Watson
Aug 28 at 12:41
See also this question: math.stackexchange.com/questions/1466539
– Watson
Aug 28 at 12:47
@Widawensen to me "solving" means presenting with proof the set of solutions (: And the empty set is a set
– Marco Flores
Nov 19 at 12:14
1
1
I wonder .. could we say the equation was "solved"? It was proved that there are no integer solutions (n>2), but on the other hand really it is some kind of negative solution..
– Widawensen
Jul 13 at 10:56
I wonder .. could we say the equation was "solved"? It was proved that there are no integer solutions (n>2), but on the other hand really it is some kind of negative solution..
– Widawensen
Jul 13 at 10:56
Beal's conjecture and the Fermat-Catalan-conjecture are obvious generalizations of Fermat's last theorem, but they are both unsolved.
– Peter
Jul 13 at 19:30
Beal's conjecture and the Fermat-Catalan-conjecture are obvious generalizations of Fermat's last theorem, but they are both unsolved.
– Peter
Jul 13 at 19:30
There is Denes' conjecture (Ribet), and FLT over $Bbb Q(sqrt 2)$ (Jarvis and Meekin). See also here and this paper.
– Watson
Aug 28 at 12:41
There is Denes' conjecture (Ribet), and FLT over $Bbb Q(sqrt 2)$ (Jarvis and Meekin). See also here and this paper.
– Watson
Aug 28 at 12:41
See also this question: math.stackexchange.com/questions/1466539
– Watson
Aug 28 at 12:47
See also this question: math.stackexchange.com/questions/1466539
– Watson
Aug 28 at 12:47
@Widawensen to me "solving" means presenting with proof the set of solutions (: And the empty set is a set
– Marco Flores
Nov 19 at 12:14
@Widawensen to me "solving" means presenting with proof the set of solutions (: And the empty set is a set
– Marco Flores
Nov 19 at 12:14
add a comment |
1 Answer
1
active
oldest
votes
up vote
-3
down vote
Yes, Fermat-Catalan-conjecture and Beal are generalizations of FLT where modularity theorem is dependent on FLT so it is difficult to say other Diophantine equations have been solved by modularity theorem. Recent Beal paper here.
answered Nov 15 at 17:23
They Rlost
11
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
-3
down vote
Yes, Fermat-Catalan-conjecture and Beal are generalizations of FLT where modularity theorem is dependent on FLT so it is difficult to say other Diophantine equations have been solved by modularity theorem. Recent Beal paper here.
answered Nov 15 at 17:23
They Rlost
11
add a comment |
up vote
-3
down vote
Yes, Fermat-Catalan-conjecture and Beal are generalizations of FLT where modularity theorem is dependent on FLT so it is difficult to say other Diophantine equations have been solved by modularity theorem. Recent Beal paper here.
answered Nov 15 at 17:23
They Rlost
11
add a comment |
up vote
-3
down vote
up vote
-3
down vote
Yes, Fermat-Catalan-conjecture and Beal are generalizations of FLT where modularity theorem is dependent on FLT so it is difficult to say other Diophantine equations have been solved by modularity theorem. Recent Beal paper here.
answered Nov 15 at 17:23
They Rlost
11
Yes, Fermat-Catalan-conjecture and Beal are generalizations of FLT where modularity theorem is dependent on FLT so it is difficult to say other Diophantine equations have been solved by modularity theorem. Recent Beal paper here.
answered Nov 15 at 17:23
They Rlost
11
answered Nov 15 at 17:23
They Rlost
11
answered Nov 15 at 17:23
They Rlost
11
answered Nov 15 at 17:23
They Rlost
11
11
add a comment |
add a comment |
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I wonder .. could we say the equation was "solved"? It was proved that there are no integer solutions (n>2), but on the other hand really it is some kind of negative solution..
– Widawensen
Jul 13 at 10:56
Beal's conjecture and the Fermat-Catalan-conjecture are obvious generalizations of Fermat's last theorem, but they are both unsolved.
– Peter
Jul 13 at 19:30
There is Denes' conjecture (Ribet), and FLT over $Bbb Q(sqrt 2)$ (Jarvis and Meekin). See also here and this paper.
– Watson
Aug 28 at 12:41
See also this question: math.stackexchange.com/questions/1466539
– Watson
Aug 28 at 12:47
@Widawensen to me "solving" means presenting with proof the set of solutions (: And the empty set is a set
– Marco Flores
Nov 19 at 12:14