DEF0223canonicalv1Squarefree ABC Check
For squarefree coprime pairs: c ≤ rad(abc). Trivially true since rad(n)=n for squarefree n.
Payload
Squarefree ABC Check
For squarefree coprime pairs: c ≤ rad(abc). Trivially true since rad(n)=n for squarefree n.
Squarefree ABC Check
Summary
For squarefree coprime pairs: c ≤ rad(abc). Trivially true since rad(n)=n for squarefree n.
Statement
\label{def:squarefree-abc}
For \emph{squarefree} coprime pairs: verify $c \le \mathrm{rad}(abc)$.
Since $\mathrm{rad}(n) = n$ for squarefree~$n$, this is automatically
satisfied.
\textbf{Lean:} \texttt{squarefree\_abc\_check}.\quad
\textbf{Registry:} III.D110.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 277 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 345-352
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Arithmetic.ABCDeep - Name:
squarefree_abc_check
Dependencies
- Canonical: III.D97
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
III.D110squarefree-abc-checkdef:squarefree-abcRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (3)
Appears in (1)
Downstream uses (computed) (6)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
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FTH0428formal theorem
FTH0428formal theoremSources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.