Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedprecheck passaudited 2026-08-16
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

λ(1729)=36 although φ(1729)=1296

Example

The number 1729 satisfies

λ(1729)=36andφ(1729)=1296.

Facts & Assumptions

Given: The factorisation 1729=7⋅13⋅19.

[L1]

Carmichael's function is the least common multiple of its prime-power values (Carmichael's function on prime powers and its least-common-multiple formula).

[L2]

Euler's totient is multiplicative on coprime positive arguments (Euler's totient is multiplicative: gcd⁡(m,n)=1 implies φ(mn)=φ(m)φ(n) for positive m,n).

Verification

technique · direct
1.1L1algebra

By [L1], λ(1729)=lcm⁡(6,12,18)=36.

2.1step 1.1L2algebra∎

By [L2], φ(1729)=6⋅12⋅18=1296, which is strictly larger than the value in step 1.1.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources