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The parity of the floor of a power of 2 multiple of sqrt(2)

Source: Romanian NO, grade ix, p.4

October 3, 2019
number theoryinequalitiesFloor

Problem Statement

Let be a natural number n. n. Prove that there exists a number k∈{0,1,2,…n} k\in\{ 0,1,2,\ldots n \} such that the floor of 2n+k2 2^{n+k}\sqrt 2 is even.
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