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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.
The Gifted Education Programme ( GEP) is an academic programme in Singapore, initially designed to identify the top 0.25% (later expanded to 0.5%, then 1%) of students from each academic year with outstanding intelligence. The tests are based on verbal, mathematical and spatial abilities (as determined by two rounds of tests ).
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).
Minkowski problem for polytopes. In the geometry of convex polytopes, the Minkowski problem for polytopes concerns the specification of the shape of a polytope by the directions and measures of its facets. [1] The theorem that every polytope is uniquely determined up to translation by this information was proven by Hermann Minkowski; it has ...
Cannonball problem. In the mathematics of figurate numbers, the cannonball problem asks which numbers are both square and square pyramidal. The problem can be stated as: given a square arrangement of cannonballs, for what size squares can these cannonballs also be arranged into a square pyramid. Equivalently, which squares can be represented as ...
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.
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 .