MathDB

4

Part of 2008 Gheorghe Vranceanu

Problems(1)

Finite partition of naturals in NT

Source:

2/5/2021
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.
number theorymodular arithmetic