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OP-10041Mathematics · generalStatus unassessed

Erdős #1163 · group theory

Describe (by statistical means) the arithmetic structure of the orders of subgroups of S n .

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9381Mathematics · generalOpen

Erdős #1162 · group theory

Give an asymptotic formula for the number of subgroups of S n . Is there a statistical theorem on their order?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9380Mathematics · generalOpen

Erdős #1160 · group theory

Let g(n) denote the number of groups of order n . If n leq 2^m then g(n) leq g(2^m) .

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9378Mathematics · generalOpen

Erdős #1158 · hypergraphs / turan number

Let K t (r) be the complete t -partite t -uniform hypergraph with r vertices in each class. Is it true that mathrm ex t(n,K t(r)) geq n^ t-r^ 1-t -o(1) for all t,r ?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9377Mathematics · generalOpen

Erdős #1157 · hypergraphs / turan number

Let t,k,r geq 2 . Let mathcal F be the family of all r -uniform hypergraphs with k vertices and s edges. Determine mathrm ex r(n, mathcal F ).

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9334Mathematics · generalOpen

Erdős #1075 · hypergraphs

Let r geq 3 . There exists c r r^ -r such that, for any epsilon 0 , if n is sufficiently large, the following holds. Any r -uniform hypergraph on n vertices with at least (1+ epsilon)(n/r)^r many edges cont…

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9315Mathematics · generalOpen

Erdős #1049 · irrationality

Let t 1 be a rational number. Is sum n=1 ^ infty frac 1 t^n-1 = sum n=1 ^ infty frac tau(n) t^n irrational, where tau(n) counts the divisors of n ?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9269Mathematics · generalOpen

Erdős #949 · ramsey theory

Let S subset mathbb R be a set containing no solutions to a+b=c . Must there be a set A subseteq mathbb R backslash S of cardinality continuum such that A+A subseteq mathbb R backslash S ?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-8919Mathematics · generalOpen

Erdős #274 · group theory / covering systems

If G is a group then can there exist an exact covering of G by more than one cosets of different sizes? (i.e. each element is contained in exactly one of the cosets)

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-8915Mathematics · generalOpen

Erdős #269 · irrationality

Let P be a finite set of primes with lvert P rvert geq 2 and let a 1<a 2< cdots = n in mathbb N : textrm if p mid n textrm then p in P . Is the sum sum n=1 ^ infty frac 1 [a 1, ldots,a n] , …

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-8914Mathematics · generalOpen

Erdős #267 · irrationality

Let F 1=F 2=1 and F n+1 =F n+F n-1 be the Fibonacci sequence. Let n 1<n 2< cdots be an infinite sequence with n k+1 /n k geq c 1 . Must sum k frac 1 F n k be irrational?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-8913Mathematics · generalOpen

Erdős #265 · irrationality

Let 1 leq a 1<a 2< cdots be an increasing sequence of integers. How fast can a n to infty grow if sum frac 1 a n quad textrm and quad sum frac 1 a n-1 are both rational?

Erdős Problems (Thomas Bloom)· Source reports OPEN

Pierce–Birkhoff conjecture

Mean value problem

Open questions on irrationality of numbers

Convergence of the Flint Hills and Cookson Hills series

Exponentials conjectures and theorems

Casas-Alvero Conjecture

Equational Theories

Mathoverflow 339137

Mathoverflow 31809

Mathoverflow 21003

Hilbert's Fifth Problem and the Hilbert–Smith Conjecture

Erdős Problem 477

Zariski Cancellation

Erdős #1163 · group theory

Erdős #1162 · group theory

Erdős #1160 · group theory

Erdős #1158 · hypergraphs / turan number

Erdős #1157 · hypergraphs / turan number

Erdős #1075 · hypergraphs

Erdős #1049 · irrationality

Erdős #949 · ramsey theory

Erdős #274 · group theory / covering systems

Erdős #269 · irrationality

Erdős #267 · irrationality

Erdős #265 · irrationality