A177986 -id:A177986 - cp's OEIS frontend

A177987 Numbers n such that quartic equation y^2=x^4+n has no solution.

2, 5, 6, 7, 10, 11, 12, 13, 14, 17, 18, 21, 22, 23, 26, 27, 29, 30, 31, 32, 34, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98

Offset: 1

Artur Jasinski, May 16 2010

nonn

Complement to this sequence see A177986.

			104 does not belong to this sequence because 27^2 = 5^4 + 104.

Cf. A054504, A081121.

A177988 Numbers n such that quartic curve y^2=x^4-n has integral points.

Original entry on oeis.org

1, 7, 12, 15, 16, 17, 31, 32, 45, 49, 56, 60, 65, 71, 72, 77, 80, 81

Offset: 1

Artur Jasinski, May 16 2010

nonn

Complement to this sequence see A177989.

Numbers n such that quartic curve y^2=x^4+n has integral points. see A177986.

Cf. A054504, A081121, A177986, A177987, A177988, A177989.

Magma
```
IntegralQuarticPoints([1,0,0,0,-81]);
```

A177989 Numbers n such that quartic equation y^2=x^4-n has no integer solution.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 70, 73, 74, 75, 76, 78, 79

Offset: 1

Artur Jasinski, May 16 2010

nonn

Complement to this sequence see A177989.

Numbers n such that the quartic curve y^2=x^4+n doesn't have integral points. see A177987.

Cf. A054504, A081121, A177986, A177987, A177988, A177989.

Magma
```
IntegralQuarticPoints([1,0,0,0,-79]);
```

cp's OEIS Frontend

A177987 Numbers n such that quartic equation y^2=x^4+n has no solution.

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A177988 Numbers n such that quartic curve y^2=x^4-n has integral points.

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Magma

A177989 Numbers n such that quartic equation y^2=x^4-n has no integer solution.

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Author

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Programs

Magma