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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.
1
7, 239, 157, 227, 40351, 62047, 46747, 59693
OFFSET
1,1
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.
EXAMPLE
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), ...
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Mia Muessig, Oct 17 2023
STATUS
approved