Number theory
For positive alpha and beta with irrational ratio, every sufficiently large integer is a finite sum of indexed terms from the sequences floor(2^n alpha) and floor(2^n beta). This establishes part (i), with the intended multiset interpretation.
Submitted by JenW1N
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«354»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos354.erdos_354.parts.i" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∀ α > 0, ∀ β > 0, Irrational (α / β) → IsAddCompleteNatSeq' (Erdos354.FloorMultiples.interleave α β 2)Original conjecture source: FormalConjectures/ErdosProblems/354.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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Individual lemmas, special cases and supporting work, shown in their original scope.
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