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#74 by Michel Marcus at Mon Nov 22 02:26:22 EST 2021
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#73 by Joerg Arndt at Mon Nov 22 01:34:32 EST 2021
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#72 by Jon E. Schoenfield at Sun Nov 21 23:31:43 EST 2021
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#71 by Jon E. Schoenfield at Sun Nov 21 23:31:40 EST 2021
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#70 by Joerg Arndt at Thu Nov 11 02:13:39 EST 2021
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#69 by Hugo Pfoertner at Wed Nov 10 16:49:16 EST 2021
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#68 by Wesley Ivan Hurt at Wed Nov 10 14:33:18 EST 2021
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#67 by Wesley Ivan Hurt at Wed Nov 10 14:32:54 EST 2021
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| NAME
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Numbers whose square can be represented in exactly one way as the sum of a square and a biquadrate (fourth power).
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| COMMENTS
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TermsNo term cannotcan be a square (see the comment from Altug Alkan in A111925).
IfAdditionally, if the terms additionally have prime factors of the form p == 3 (mod 4), which are in A002145, then they must appear in the prime divisor sets of x and y too.
The special prime factor 2 has the same behavior. Means: If, i.e., if the term is even, x and y must be even too. (End)
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| STATUS
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proposed
editing
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#66 by Karl-Heinz Hofmann at Sun Nov 07 04:53:24 EST 2021
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#65 by Karl-Heinz Hofmann at Sun Nov 07 04:52:52 EST 2021
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| COMMENTS
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If the terms additionally have prime factors of the form p == 3 (mod 4), which are in A002145, then they must appear in the prime divisor sets of x and y too. (End).
The special prime factor 2 has the same behavior. Means: If the term is even, x and y must be even too. (End)
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| CROSSREFS
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Cf. A000290, A000583, A271576, A180241., A271576 (all solutions).
Cf. A346110 (4 solutions), A346115A348655 (the least5 solutions).
Cf. A346115 (the least solutions).
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| STATUS
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approved
editing
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