Pith Number

pith:AADT3F7E

pith:2013:AADT3F7E7JQKPZGENMLMKQUAQV

not attested not anchored not stored refs pending

On the congruence $1^m + 2^m + \dotsb + m^m \equiv n \pmod{m}$ with $n | m$

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

arxiv:1309.7941 v7 · 2013-09-30 · 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{AADT3F7E7JQKPZGENMLMKQUAQV}

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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.

Cited by

1 paper in Pith

Port Fillings for Primary Pseudoperfect Numbers

Receipt and verification

First computed	2026-05-18T01:48:06.909794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00073d97e4fa60a7e4c46b16c54280856b3e5b89955b3443426d117dc0f3dfae

Aliases

arxiv: 1309.7941 · arxiv_version: 1309.7941v7 · doi: 10.48550/arxiv.1309.7941 · pith_short_12: AADT3F7E7JQK · pith_short_16: AADT3F7E7JQKPZGE · pith_short_8: AADT3F7E

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/AADT3F7E7JQKPZGENMLMKQUAQV \
  | 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: 00073d97e4fa60a7e4c46b16c54280856b3e5b89955b3443426d117dc0f3dfae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7a0e4e93a5e524330fe5c57699e5e25a11d2d4effd27a5632659fa5800f6d0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-30T17:49:15Z",
    "title_canon_sha256": "bfbfdfaf2942e1fcfa7cce29ce06bc9ba6724daaab1795c88d64f468d6af04a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7941",
    "kind": "arxiv",
    "version": 7
  }
}