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Eric Naslund
Eric Naslund
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Nasty Integer Points on the Elliptic Curve $y^2=x^3+17$.

I came across the problem "find all integer solutions to $y^2=x^3+17$."

I've tried several things, without any success, and I was hoping that someone could help out. (Some ideas or a reference for where to find it are both appreciated)

By numerical calculation I have found that the following integer points $(x,y)$ lie on the curve

$(-1,4)$, $(-2,3)$, $(2,5)$, $(4,9)$, $(8,23)$, $(43,282)$, $(52,375)$, $(5234,378661)$ and this is probably all of them.

Thanks

Remark: Although I believe that this problem is very difficult, I am unsure if it is at the right level for MO, so before going too far someone tell me if it's okay to just leave it or if I should delete and repost on math stack exchange.

Nasty Elliptic Curve

I came across the problem "find all integer solutions to $y^2=x^3+17$."

I've tried several things, without any success, and I was hoping that someone could help out. (Some ideas or a reference for where to find it are both appreciated)

By numerical calculation I have found that the following integer points $(x,y)$ lie on the curve

$(-1,4)$, $(-2,3)$, $(2,5)$, $(4,9)$, $(8,23)$, $(43,282)$, $(52,375)$, $(5234,378661)$ and this is probably all of them.

Thanks

Remark: Although I believe that this problem is very difficult, I am unsure if it is at the right level for MO, so before going too far someone tell me if it's okay to just leave it or if I should delete and repost on math stack exchange.

Integer Points on the Elliptic Curve $y^2=x^3+17$.

I came across the problem "find all integer solutions to $y^2=x^3+17$."

I've tried several things, without any success, and I was hoping that someone could help out. (Some ideas or a reference for where to find it are both appreciated)

By numerical calculation I have found that the following integer points $(x,y)$ lie on the curve

$(-1,4)$, $(-2,3)$, $(2,5)$, $(4,9)$, $(8,23)$, $(43,282)$, $(52,375)$, $(5234,378661)$ and this is probably all of them.

Thanks

Source Link
Eric Naslund
Eric Naslund
  • 11.4k
  • 1
  • 66
  • 106

Nasty Elliptic Curve

I came across the problem "find all integer solutions to $y^2=x^3+17$."

I've tried several things, without any success, and I was hoping that someone could help out. (Some ideas or a reference for where to find it are both appreciated)

By numerical calculation I have found that the following integer points $(x,y)$ lie on the curve

$(-1,4)$, $(-2,3)$, $(2,5)$, $(4,9)$, $(8,23)$, $(43,282)$, $(52,375)$, $(5234,378661)$ and this is probably all of them.

Thanks

Remark: Although I believe that this problem is very difficult, I am unsure if it is at the right level for MO, so before going too far someone tell me if it's okay to just leave it or if I should delete and repost on math stack exchange.