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Home » Olympiad Section » Number Theory » Number Theory Unsolved Problems

x^2-y^3=n
Moderators: High School Olympiad Moderators, amfulger, Arne, darij grinberg, freemind, harazi, Megus, N.T.TUAN, orl, pbornsztein, ZetaX

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kiemkhach
P versus NP

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x^2-y^3=n
my friend

find $n \in Z$ such that $x^2-y^3=n$ has a integral solution.

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Posted: Thu Feb 17, 2005 10:33 pm

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Pascual2005
Navier-Stokes Equations

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it seems like an open problem to me, at least i am sure it uses advanced algebraic number theory.

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Posted: Fri Feb 18, 2005 4:30 am

RobertuX
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Re: x^2-y^3=n
my friend

kiemkhach wrote:

find $n \in Z$ such that $x^2-y^3=n$ has a integral solution.

Well, I think you need to uses a stronger language to define the problem, because takin $x=0$ and $y=-1$ you get that one $n$ is $n=1$ , plese explain better the problem, if not this problem ... is for newbies. Wink

Wink

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Posted: Fri Feb 18, 2005 8:10 am

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fleeting_guest
Yang-Mills Theory

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it is a famous unsolved problem.

kiemkhach wrote:

find $n \in Z$ such that $x^2-y^3=n$ has a integral solution.

Good luck. See http://arXiv.org/abs/math/0005139

Also relevant is Tunnell's solution (conditional on Birch-Swinnerton-Dyer conjecture for elliptic curves) of the Congruent Number Problem, i.e. which $n$ are values of $x^3 + y^3$ .

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Posted: Fri Feb 18, 2005 2:27 pm

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