Pith Number

pith:CK2QKVEP

pith:2013:CK2QKVEPV2CF5X4HP4MU7EOQIS

not attested not anchored not stored refs pending

On the congruence $\sum_{j=1}^{n-1} j^{k(n-1)} \equiv -1 \pmod n $. k-strong Giuga and k-Carmichael numbers

Antonio M. Oller-Marc\'en, Jos\'e Mar\'ia Grau

arxiv:1311.3522 v1 · 2013-11-14 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CK2QKVEPV2CF5X4HP4MU7EOQIS}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:07:10.677187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12b505548fae845edf877f194f91d0448757d1c40f782d45584c7bf04cb4bfe4

Aliases

arxiv: 1311.3522 · arxiv_version: 1311.3522v1 · doi: 10.48550/arxiv.1311.3522 · pith_short_12: CK2QKVEPV2CF · pith_short_16: CK2QKVEPV2CF5X4H · pith_short_8: CK2QKVEP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CK2QKVEPV2CF5X4HP4MU7EOQIS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 12b505548fae845edf877f194f91d0448757d1c40f782d45584c7bf04cb4bfe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c64bf3b0368da68c249ed6cf2fd3bdf851cda90f2c556da14d4f5cd8aa85488",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-14T14:52:57Z",
    "title_canon_sha256": "07c4a81d73c8df4aeed8f53dd1f9af168609b594ce710bff05048cf3918eb148"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3522",
    "kind": "arxiv",
    "version": 1
  }
}