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Finite partition of naturals in NT

Source:

February 5, 2021
number theorymodular arithmetic

Problem Statement

Find the largest natural number k k which has the property that there is a partition of the natural numbers ⋃1≤j≤kVj, \bigcup_{1\le j\le k} V_j, an index i∈{1,…,k} i\in\{ 1,\ldots ,k \} and three natural numbers a,b,c∈Vi, a,b,c\in V_i, satisfying a+2b=4c. a+2b=4c.
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