Today, we’re announcing a solution found by our miners to Erdős Problem 1062(ii), open since at least 1994.
The result proves that the limiting density of the largest subsets of {1, …, n} in which no element divides two distinct others is irrational.
Verified in Lean through Conjectures. Full proofs below.
Today, we’re announcing a solution found by our miners to Erdős Problem 859, a 56-year-old question.
Let dₜ be the density of integers whose distinct divisors can sum to t. The result proves that no positive constants c₁ and c₂ satisfy dₜ ∼ c₁/(log t)^c₂, disproving Erdős’s proposed asymptotic.
Verified in Lean through Conjectures. Full proof below.
Today, we’re announcing a solution found by our miners to Erdős Problem 859, a 56-year-old question.
Let dₜ be the density of integers whose distinct divisors can sum to t. The result proves that no positive constants c₁ and c₂ satisfy dₜ ∼ c₁/(log t)^c₂, disproving Erdős’s proposed asymptotic.
Verified in Lean through Conjectures. Full proof below.
Today, we’re announcing a solution found by our miners to both parts of Erdős Problem 14, open for over 34 years.
The result proves a square-root lower bound on exceptions to unique representation as a sum of two elements of any set of natural numbers.
Verified in Lean through Conjectures. Full proofs below.