Problems

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additive_bases/: Representation functions of sets of integers: additive bases and the Erdos-Turan basis conjecture, Sidon and B_h sets in which sums or differences are almost distinct, and complete sequences whose subset sums represent every large integer.

additive_combinatorics/: Sumsets and difference sets, densities and sum-free sets, arithmetic progressions in dense sets of integers together with the coloring problems that force them (van der Waerden numbers), difference bases and perfect rulers, and sets with distinct subset sums.

analysis/: Entire and complex functions, real functions and measure, exponential sums and series, and the few purely probabilistic and topological problems that carry no subject co-tag.

arithmetic_functions/: Problems on the values, distribution and iterates of named arithmetic functions — Euler's totient, the sum and number of divisors, counts of prime factors, the largest prime factor — along with general additive and multiplicative functions and perfect, amicable and aliquot-type questions.

covering_systems/: Systems of congruences covering the integers, exact and disjoint coverings, the minimum modulus problem, and the analogous exact coverings of a group by cosets.

diophantine_problems/: Problems asking whether an equation has integer solutions or whether integers of a given algebraic shape exist — squares and perfect powers, powerful and squarefree numbers, sums of k-th powers, products of consecutive integers, and base and digit representations.

discrepancy/: The Erdos discrepancy problem and its relatives: how unbalanced a plus/minus one coloring must become along arithmetic progressions, dilates and set systems, and irregularities of distribution of sequences and of graph colorings.

discrete_geometry/: Point configurations, lines and incidences, convex position and convex bodies, coverings, packings and geometric measure problems, together with Euclidean Ramsey theory and the colorings of the plane and of R^n descended from the Hadwiger-Nelson problem.

distance_problems/: Distinct, repeated and unit distances among finite point sets, diameters and nearest-neighbor conditions, and distance problems for points in convex position.

divisors/: Divisor functions and the distribution of divisors, multiplication tables, sets of multiples, primitive sets in which no element divides another, and other sets of integers defined by divisibility or coprimality conditions.

extremal_graph_theory/: Turan-type extremal problems for graphs and hypergraphs, forbidden subgraphs and edge counts, cycles and girth, degree and subgraph-counting conditions, planarity, and structural questions such as the Erdos-Hajnal conjecture.

factorials_binomials/: Divisibility, prime factorization and digit arithmetic of factorials, binomial coefficients, and products of consecutive integers.

graph_coloring/: Chromatic number of graphs and hypergraphs, list and edge colorings, color-critical graphs, and the interaction of coloring with girth and cycles; colorings of the plane and of R^n are filed with discrete geometry.

group_theory/: Combinatorial problems about groups, including non-commuting graphs of groups; exact coverings of a group by cosets are filed with covering systems.

integer_sequences/: Problems on sets and sequences of integers defined by divisibility, coprimality, gcd or lcm, or residue conditions, or by avoiding a pattern, asking for their density, counting function, gaps or growth, including covering-congruence and sieve questions.

irrationality/: Irrationality and transcendence of series and constants, irrationality sequences, and how well real numbers can be approximated by rationals.

number_theory/: The general number theory problems fitting none of the three themed folders, including questions about real numbers, reciprocal sums as points, irrational rotations and floor sequences, quadratic residues and character sums, and other one-off constructions.

polynomials/: Extremal and approximation problems for polynomials, including coefficient and norm bounds, zero distribution, and random polynomials.

primes/: Distribution of the primes, prime gaps, and prime values and patterns in arithmetic sequences.

ramsey_theory/: Ramsey numbers for graphs and hypergraphs, off-diagonal and induced variants, and monochromatic structures forced by colorings of the integers of Schur and Rado type; Euclidean Ramsey problems and colorings of the plane are filed with discrete geometry.

set_systems/: Finite set systems and hypergraphs: sunflowers and delta-systems, intersecting and union-free families, antichains, property B, block designs, Latin squares and finite projective planes, together with the general combinatorics problems the site tags no more finely.

set_theory/: Infinite graphs and hypergraphs, partition calculus and infinite Ramsey theory, cardinal arithmetic, and problems whose answers are independent of the usual axioms of set theory.

unit_fractions/: Egyptian fractions and reciprocal sums, including the Erdos-Straus conjecture and the Erdos-Graham problems on representing rationals as sums of unit fractions.

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Each page is E<nnnn>.md — the problem's erdosproblems.com number zero-padded to four digits, so E0570.md is Problem 570 and the pages sort in the site's order. Pages sit one level deep in area folders; a problem's folder follows from its site tags by the ordered rules in scripts/taxonomy.json, with a small override table for the exceptions. A page records the statement, the current status with the evidence behind it, the known results with their sources, and working notes toward the problem while it stays open. The site's problem page is the first reference for the statement, status, prize, and remarks; the results a page cites link to their pages under library/.