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58 problems · 2/2NumberSourcesGraph view
declared open · formalizederdos:1101
Does there exist a good pairwise-coprime sequence unu_n with ∑1/un<∞\sum 1/u_n < \infty and polynomial growth? What if one only requires un≤eo(n)u_n \le e^{o(n)}?
number theoryN/A4 sources
declared open · formalizederdos:1133
Must every sufficiently large node set admit bounded labels that force any polynomial fitting almost all labels at degree below (1+ε)n(1+\varepsilon)n to have arbitrarily large uniform norm? Claimed via Beurling density for Bernstein spaces.
analysispolynomialsN/A4 sources
declared openerdos:1151
Let Lnf\mathcal{L}^nf be the Lagrange interpolation polynomials of a continuous ff on the Chebyshev nodes. Prove that, for any closed A⊆[−1,1]A\subseteq [-1,1], there exists a continuous function ff such that AA is the set of limit points of Lnf(x)\mathcal{L}^nf(x).
analysispolynomialsN/A3 sources
declared openerdos:1177
For a finite forbidden triple system GG, what exact uncountable chromatic cardinalities occur among GG-free triple systems, and how do those spectra interact? The revised manuscript answers the three exact-cardinal questions and claims a complete spectrum dichotomy.
set theorychromatic numberhypergraphsN/A3 sources
declared openerdos:1186
What is the minimum asymptotic density δk\delta_k of monochromatic kk-term arithmetic progressions in every two-colouring of {1,…,n}\{1, \dots, n\}? The exact certificate gives δ3=117/2192\delta_3 = 117/2192, matching the known 548-bead colouring.
additive combinatoricsarithmetic progressionspossible2 sources
declared open · formalizederdos:1188
Estimate the number F(x)F(x) of minimal distinct covering systems whose moduli all lie in [1,x][1, x]. The candidate proof gives log⁡log⁡F(x)/log⁡x→1\log\log F(x)/\log x \to 1, i.e. F(x)=exp⁡(x1+o(1))F(x) = \exp(x^{1+o(1)}).
number theorycovering systemspossible4 sources
declared openerdos:1189
For irreducible covering sets of size kk, determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.
number theorycovering systemspossible2 sources
declared open · formalizederdos:1201
Is it true that for every ϵ,η>0\epsilon,\eta>0 there exists a kk such that the density of nn for which P(n(n+1)⋯(n+k))>n1−ϵP(n(n+1)\cdots(n+k))>n^{1-\epsilon} is at least 1−η1-\eta, where P(m)P(m) is the greatest prime divisor of mm? A short argument via the Matomäki-Radziwiłł theorem establishes the lower-density version.
number theoryprimespossible4 sources