Erdős Problem #978
If k>3 (and k ≠ 2^l), and for all primes p there exists n such that p^k-2nmid f(n), then are there infinitely many n for which f(n) is (k-2)-power-free?
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Erdős problems (Erdos problems) you can work on with AI
Paul Erdős posed hundreds of problems, many with cash prizes. Thomas Bloom collects them at erdosproblems.com, and a community database (teorth/erdosproblems) tracks their status. Most of the open ones listed here have Lean statements in Formal Conjectures; each imported page shows the status from erdosproblems.com, the prize if there is one, and what kind of progress would count.
Source: erdosproblems.com (Thomas Bloom). Licence: Lean statements from Formal Conjectures (Apache 2.0); status data from the community database teorth/erdosproblems (Apache 2.0).
Erdős Problem #979
Let k ≥ 2, and let f_k(n) count the number of solutions to n = p_1^k + … + p_k^k, where the p_i are prime numbers. Is it true that limsup f_k(n) = ∞?
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Erdős Problem #98
Let h(n) be such that any n points in ℝ^2, with no three on a line and no four on a circle, determine at least h(n) distinct distances. Does h(n)/n→ ∞?
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Erdős Problem #982
If n distinct points in ℝ^2 form a convex polygon then some vertex has at least lfloorn/2⌋ different distances to other vertices.
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Erdős Problem #983
Let n≥ 2 and π(n)<k≤ n. Let f(k,n) be the smallest integer r such that in any A⊆ 1,…,n of size lvert Arvert=k there exist primes p_1,…,p_r such that >r many a∈ A are only divisible by primes from p_1,…,p_r. In general, estimate f(k,n), particularly when π(n)+1<k=o(n). This is the second part.
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Erdős Problem #985
Is it true that, for every prime p, there is a prime q ≤ p which is a primitive root modulo p?
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Erdős Problem #99
For sufficiently large n, is it the case that any set of n points with minimum distance 1 that minimizes diameter must contain an equilateral triangle of side length 1?
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Erdős Problem #995
Erdős Problem 995: For every lacunary sequence (n_k) of integers and every f ∈ L^2([0,1]) with ∫_0^1 f = 0, is it true that for almost all α, Σ_k < N f(α n_k) = o (N √(loglog N))?
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Erdős Problem #996
Does there exists a positive constant C such that for all f ∈ L²[0,1] and all lacunary sequences n, if ‖f - fₖ‖₂ = O(1 / log log log k ^ C), then for almost every x, lim ∑ k ∈ Finset.range N, f (n k • x)) / N = ∫ t, f t ∂t?
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