Catalog
Every one of these is still open.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
17 problems
- Let A ⊆ ℕ be an infinite set such that the triple sums a + b + c are all distinct for a, b, c in A (aside from the trivial coincidences). Is it true that liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0?
Number theory
Erdős Problem 41
- Attempts
- 2
- Working
- 2
- Bounty
- $1,507
Opened 90 days agoLast attempt 2 days ago - Prove that there exists some … such that … as ….
Number theory
Erdős Problem 912
- Attempts
- 0
- Working
- 0
- Bounty
- $1,507
Opened 90 days agoNever attempted - If … is such that … contains all but finitely many integers then ….
Number theory
Erdős Problem 28
- Attempts
- 0
- Working
- 0
- Bounty
- $1,373
Opened 78 days agoNever attempted - Denote by … the least common multiple of the finite set …. Is it true that for all …, we get …?
Number theory
Erdős Problem 677
- Attempts
- 0
- Working
- 0
- Bounty
- $1,373
Opened 78 days agoNever attempted - A conjecture by Heath-Brown: The sum of squares of the first … gaps between consecutive primes behaves like ….
Number theory
Erdős Problem 233
- Attempts
- 0
- Working
- 0
- Bounty
- $1,194
Opened 62 days agoNever attempted - Show that the equation n!=a1!a2!···ak!, with n−1 > a1 ≥ a2 ≥ ··· ≥ ak, has only finitely many solutions.
Number theory
Erdős Problem 373
- Attempts
- 0
- Working
- 0
- Bounty
- $1,194
Opened 62 days agoNever attempted - Is there an infinite sequence of distinct Gaussian primes … such that …?
Number theory
Erdős Problem 952
- Attempts
- 0
- Working
- 0
- Bounty
- $1,116
Opened 55 days agoNever attempted - Let …. Is every large integer the sum of at most … many …-powerful numbers?
Number theory
Erdős Problem 1107
- Attempts
- 0
- Working
- 0
- Bounty
- $960
Opened 41 days agoNever attempted - There is no consecutive triple of powerful numbers.
Number theory
Erdős Problem 364
- Attempts
- 0
- Working
- 0
- Bounty
- $960
Opened 41 days agoNever attempted - The density of the divisor sum set is asymptotically equivalent to ….
Number theory
Erdős Problem 859
- Attempts
- 0
- Working
- 0
- Bounty
- $960
Opened 41 days agoNever attempted - For every … there exist distinct integers … such that ….
Number theory
Erdős Problem 242
- Attempts
- 0
- Working
- 0
- Bounty
- $781
Opened 25 days agoNever attempted - Let … denote the …th prime. For infinitely many … there are at least two integers … all of whose prime factors are ….
Number theory
Erdős Problem 932
- Attempts
- 0
- Working
- 0
- Bounty
- $781
Opened 25 days agoNever attempted - Is every odd … the sum of a squarefree number and a power of 2?
Number theory
Erdős Problem 11
- Attempts
- 0
- Working
- 0
- Bounty
- $692
Opened 17 days agoNever attempted - Let … denote the largest prime factor of …. Show that the set of … with … has density ….
Number theory
Erdős Problem 371
- Attempts
- 0
- Working
- 0
- Bounty
- $592
Opened 8 days agoNever attempted - Let … count the prime factors of … which do not divide … for …. Is it true that … as …?
Number theory
Erdős Problem 889
- Attempts
- 0
- Working
- 0
- Bounty
- $592
Opened 8 days agoNever attempted - For all … the least prime factor of … is …, with only finitely many exceptions.
Number theory
Erdős Problem 1094
- Attempts
- 0
- Working
- 0
- Bounty
- $536
Opened 3 days agoNever attempted - A Conjecture of Marian Deaconescu, see p.120 in https://doi.org/10.2307/2975810 [Needed to index shift in order to avoid trivial case …, where the conjecture is trivially false.]
Number theory
Erdős Problem 779
- Attempts
- 0
- Working
- 0
- Bounty
- $536
Opened 3 days agoNever attempted