We observe and prove that Fibonacci numbers F (n) for odd indices n exhibit a striking partition modulo 24, with strong bias toward residue classes connected to Heegner numbers and class field theory. Specifically, for all odd n ∈ ℕ, we have F (n) ∈ 1, 2, 5, 10, 13, 17 (mod 24), and the Anti-Heegner residues 5, 13, 17 appear with frequency ≈ 50% in one Pisano period. We provide rigorous proofs of quadratic residue exclusion via Pisano periods and the Chinese Remainder Theorem, prove the exact partition via periodicity and induction, and demonstrate that all nine Heegner discriminants naturally map to Anti-Heegner residues modulo 24.
Thomas Kaden (Sun,) studied this question.
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