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.
29 problems
- Let … count the number of solutions to … for prime … and …. Show that ….
Combinatorics
Erdős Problem 236
- Attempts
- 0
- Working
- 0
- Bounty
- $1,507
Opened 90 days agoNever attempted - 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 - Erdős [Er46] asked whether every set of … distinct points in … determines … many distinct distances.
Convex & discrete geometry
SolvedErdős Problem 89
- Attempts
- 1
- Working
- 1
- Bounty
- $1,194
Opened 62 days agoLast attempt last month - Let … be a sequence of integers such that … and …. Then, for all sufficiently large …, ….
Sequences & series
Erdős Problem 243
- Attempts
- 0
- Working
- 0
- Bounty
- $1,116
Opened 55 days agoNever attempted - Let …. If the edges of … are …-coloured then there exist … vertices with at least one colour missing on the edges of the induced …. In other words, there is no balanced colouring. A conjecture of Erdős and Gyárfás [ErGy99].
Combinatorics
Erdős Problem 617
- Attempts
- 0
- Working
- 0
- Bounty
- $1,116
Opened 55 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 …, and let … denote the size of the largest subset of … such that no subset of size … has the same pairwise greatest common divisor between all elements. Erdős [Er64] proved that … for some constant …, and conjectured this should also be an upper bound; here we state the conjectural upper bound for all …. See also…
Combinatorics
Erdős Problem 535
- 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 … be the greedy Sidon sequence: we begin with … and iteratively include the next smallest integer that preserves the Sidon property (i.e. there are no non-trivial solutions to …). What is the order of growth of …? Is it true that … for all … and large …?
Combinatorics
Erdős Problem 340
- Attempts
- 0
- Working
- 0
- Bounty
- $692
Opened 17 days agoNever attempted - …
Combinatorics
Erdős Problem 82
- Attempts
- 0
- Working
- 0
- Bounty
- $692
Opened 17 days agoNever attempted - Let … be a group, and let … be a finite system of left cosets of subgroups … of …. Herzog and Schönheim conjectured that if … forms a partition of … with …, then the indices … cannot be distinct.
Group theory
Erdős Problem 274
- Attempts
- 3
- Working
- 2
- Bounty
- $636
Opened 12 days agoLast attempt yesterday - Let … be a finite set of size … and … be such that there is a function … so that for every … with … we have …. Prove that ….
Combinatorics
Erdős Problem 624
- Attempts
- 1
- Working
- 1
- Bounty
- $636
Opened 12 days agoLast attempt 21 days ago - If … distinct points in … form a convex polygon then some vertex has at least … different distances to other vertices.
Convex & discrete geometry
Erdős Problem 982
- Attempts
- 0
- Working
- 0
- Bounty
- $636
Opened 12 days agoNever attempted - Any graph on … vertices can be decomposed into … many edge-disjoint cycles and edges.
Combinatorics
In reviewErdős Problem 184
- Attempts
- 1
- Working
- 1
- Bounty
- $592
Opened 8 days agoLast attempt 3 days ago