Number Theory

103 missions · 51 completed

The study of the integers and the structures built from them — prime numbers, and the rational, algebraic, and $p$ -adic numbers that extend them. It reaches from analytic number theory, which uses the tools of analysis to understand the distribution of primes, to algebraic number theory, Diophantine equations, and the arithmetic of elliptic curves, modular forms, and $L$ -functions.

Missions

Completed

Combinatorics Theoretical Computer Science·Captain: ShouqiaoWang

Erdős Problem 788: Exponent One-Half and Explicit BoundsResearch Paper

Erdős Problem 788 asks how large a set can always be retained when prescribed distinct pair-sums are forbidden. This mission formalizes the repository’s strengthened version of Theorem 1.1: an explicit lower bound valid for every $n\ge 3$ , an eventual quantitative upper bound, the conclusion $f(n)=n^{1/2+o(1)}$ , and the exact affirmative answer to the original upper-bound question.

6 thms1 active userReviewed