trailProving the Collatz conjecture is at least as difficult as proving Baker's theorem on linear forms in logarithms.
Reduction to transcendence theory· for
The absence of nontrivial Collatz cycles implies a nontrivial lower bound on |2^n − 3^m| for all natural numbers n, m.
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Every known nontrivial lower bound for |2^n − 3^m| relies on transcendence theory such as Baker's method.
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All known proofs that the Collatz map has no m-cycles for small m rely on Baker's theorem on linear forms in logarithms.
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Implied bound falls short of Baker· against
The lower bound on |2^n − 3^m| implied by the weak Collatz conjecture is far weaker than the bound Baker's theorem gives.
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claim · evaluativeA judgment of worth or quality against some standard: good, fair, effective.constitution →claim page ↗︎
Proving the Collatz conjecture is at least as difficult as proving Baker's theorem on linear forms in logarithms.
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