cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A179447 Smallest values d such that the equation d =x^5-y^2 has exactly n distinct nonnegative integer solutions.

Original entry on oeis.org

2, 1, 7, 1044976, 11331151
Offset: 0

Views

Author

Artur Jasinski, Jul 14 2010

Keywords

Comments

a(0)=2 because no integer solutions x^5-y^2 = 2;
a(1)=1 because 1=1^5-0^2;
a(2)=7 because 7=2^5-5^2 and 7=8^5-181^2;
a(3)=1044976 because 1044976=16^5-60^2 and 1044976=20^5-1468^2 and 1044976=41^5-10715^2;
a(4)=11331151 because 11331151=35^5-6418^2 and 11331151=40^5-9543^2 and 11331151=56^5-23225^2 and 11331151=386^5-2927305^2.

Links

Crossrefs

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179406, A179407, A179408, A179439.

A198393 Rank of hyperelliptic curve y^2 = x^5 - n.

Original entry on oeis.org

1, 0, 0, 0, 2, 0, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 2, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 0, 0, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 1, 3, 1, 2, 1, 0, 0, 1, 0, 2, 3, 1, 0, 2, 1, 1, 0, 1, 1, 2, 1, 1, 3, 1, 0, 1, 2, 0, 0, 1, 2, 1, 0, 1, 1, 1, 1
Offset: 1

Views

Author

Artur Jasinski, Oct 24 2011

Keywords

Comments

If a(n)=0 number of rational points of hyperelliptic curve is finite and if a(n)<>0 then is infinite. For n when a(n)=0 see A198394.

Crossrefs

Cf. A179406, A179407, A179408.

Programs

  • Magma
    _ := PolynomialRing(Rationals());
for n := 1 to 100 do
C := HyperellipticCurve(x^5-n);
J := Jacobian(C);
RankBound(J)

A179448 Numbers d such that the equation d =x^5-y^2 has more than 2 distinct nonnegative integer solutions.

Original entry on oeis.org

1044976, 1541468, 11331151, 15579791, 16410368, 33543196, 46539324, 72697500, 302272796, 528292607
Offset: 1

Views

Author

Artur Jasinski, Jul 14 2010

Keywords

Examples

			a(1)=1044976 because 1044976=16^5-60^2 and 1044976=20^5-1468^2 and 1044976=41^5-10715^2;
a(3)=11331151 because 11331151=35^5-6418^2 and 11331151=40^5-9543^2 and 11331151=56^5-23225^2 and 11331151=386^5-2927305^2.

Links

Crossrefs

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179406, A179407, A179408, A179439, A179447.
Previous Showing 21-23 of 23 results.

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