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User: Mia Muessig

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A366703 List of quadruples (a,b,c,d) with a^4 + b^4 = c^4 + d^4, a < c < d < b, a,b,c,d prime, listed in order of the largest term b.

Original entry on oeis.org

7, 239, 157, 227, 40351, 62047, 46747, 59693
Offset: 1

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Author

Mia Muessig, Oct 17 2023

Keywords

Comments

See A255352 for quadruples which do not necessarily consist of prime numbers. There are infinitely many such quadruples, because if (a, b, c, d) is in the sequence, so is (m*a, m*b, m*c, m*d). It is unknown whether there are infinitely many quadruples which consist only of prime numbers. The two given quadruples are the only ones with a^4 + b^4 = c^4 + d^4 <= 10^24.

Examples

			The quadruples (a,b,c,d), listed in order of increasing b = max{a,b,c,d}, are
  (7, 239, 157, 227),
  (40351, 62047, 46747, 59693), ...

Links

Crossrefs

Cf. A018786, A255351, A255352.

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