Pith Number

pith:YKJ6NN2E

pith:2017:YKJ6NN2EIG6G6DXBH5LCNPVQKJ

not attested not anchored not stored refs pending

Powerful numbers in $(1^{\ell}+q^{\ell})(2^{\ell}+q^{\ell})\cdots (n^{\ell}+q^{\ell})$

Qing-Qing Zhao, Quan-Hui Yang

arxiv:1706.03350 v1 · 2017-06-11 · 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{YKJ6NN2EIG6G6DXBH5LCNPVQKJ}

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	2026-05-18T00:42:37.719189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c293e6b74441bc6f0ee13f5626beb0525bad540b01b3fcd9a02a59d94364a982

Aliases

arxiv: 1706.03350 · arxiv_version: 1706.03350v1 · doi: 10.48550/arxiv.1706.03350 · pith_short_12: YKJ6NN2EIG6G · pith_short_16: YKJ6NN2EIG6G6DXB · pith_short_8: YKJ6NN2E

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/YKJ6NN2EIG6G6DXBH5LCNPVQKJ \
  | 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: c293e6b74441bc6f0ee13f5626beb0525bad540b01b3fcd9a02a59d94364a982

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "699e14ea0d3cca19b9a0e80bd3adea8839ffb5da46b23ac97233ea17126bee93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-06-11T13:19:21Z",
    "title_canon_sha256": "d54db3039046d381d44fc493b5359eccf8979a8da2dfc9f6ab84fbccf0f82abd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.03350",
    "kind": "arxiv",
    "version": 1
  }
}