Number of squares $\bmod n$

formal-conjectures · oeis · ams-11

The number of squares modulo $n$.
This is the cardinality of the set $\{k^2 \bmod n \mid k \in \{0, 1, \dots, n-1\}\}$.

$n^2 \equiv 1 \pmod{a(n)(a(n)-1)}$ if and only if $n$ is an odd prime.
- Thomas Ordowski, Jun 08 2017

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A000224
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/224.lean
Local target: Corpus.OEIS224.conjecture
Source SHA-256: 405ed5e76a0c678c404a19aa288a86b30f3a6b3194297f1228a51ee336460184
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

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