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A necessary condition for a congruent number of the form $8k+3$

math.NT · 2026-04-25 · unverdicted · novelty 4.0

For square-free n = p1...pt q with pi ≡1 mod 8 and q≡3 mod 8, if n is a congruent number then the 2-part of the class number of Q(sqrt(-n)) is congruent modulo 2^k to that of Q(sqrt(-p1...pt)) via a modified Rédei matrix.

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  • A necessary condition for a congruent number of the form $8k+3$ math.NT · 2026-04-25 · unverdicted · none · ref 25

    For square-free n = p1...pt q with pi ≡1 mod 8 and q≡3 mod 8, if n is a congruent number then the 2-part of the class number of Q(sqrt(-n)) is congruent modulo 2^k to that of Q(sqrt(-p1...pt)) via a modified Rédei matrix.