MathDB

A. 744

Part of KoMaL A Problems 2018/2019

Problems(1)

Vectors With Special Properties

Source: KöMaL A. 744

3/19/2022
Show that for every odd integer N>5N>5 there exist vectors u,v,w\bf u,v,w in (three-dimensional) space which are pairwise perpendicular, not parallel with any of the coordinate axes, have integer coordinates, and satisfy N=∣u∣=∣v∣=∣w∣.N\bf =|u|=|v|=|w|.
Based on problem 2 of the 2018 Kürschák contest
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