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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Upper Bound on minimum number of lattice points

How to derive an upper bound on the minimum number $n(k,d)$ of lattice points in $d$-dimensions such that there are some $k$ of these points which have a lattice point centroid.
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