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The main difficulty is that, in order to solve the problem, the square-roots should be computed to a high accuracy, which may require a large number of bits. The problem is mentioned in the Open Problems Garden. [4] Blomer [5] presents a polynomial-time Monte Carlo algorithm for deciding whether a sum of square roots equals 0.
Subset sum problem. The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-hard.
Hilbert's seventeenth problem. Hilbert's seventeenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression of positive definite rational functions as sums of quotients of squares. The original question may be reformulated as:
Erdős distinct distances problem. In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 [1] [2] and almost proven by Larry Guth and Nets Katz in 2015. [3] [4] [5]
In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of , the set of pairwise sums or , the set of pairwise products form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants c and such that for any non-empty set.
Barycentric-sum problem. Combinatorial number theory deals with number theoretic problems which involve combinatorial ideas in their formulations or solutions. Paul Erdős is the main founder of this branch of number theory. Typical topics include covering system, zero-sum problems, various restricted sumsets, and arithmetic progressions in a ...
Mary Winston Jackson (1921–2005), degree from Hampton Institute. Eleanor Green Dawley Jones (1929-2021), degrees from Howard University, Syracuse University (PhD). Abdulalim A. Shabazz (1927–2014), degrees from Lincoln University (Pennsylvania), Massachusetts Institute of Technology (MIT), Cornell University (PhD).
Zero-sum problem. In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group G and a positive integer n, one asks for the smallest value of k such that every sequence of elements of G of size k contains n terms that sum to 0 .