MathDB

56

Part of 1979 IMO Longlists

Problems(1)

Existence of natural - involves floor function, sqrt{2}

Source: ILL 1979 - Problem 56.

6/5/2011
Show that for every n∈Nn\in\mathbb{N}, n2−⌊n2⌋>12n2n\sqrt{2}-\lfloor n\sqrt{2}\rfloor>\frac{1}{2n \sqrt{2}} and that for every ϵ>0\epsilon >0, there exists an n∈Nn\in\mathbb{N} such that n2−⌊n2⌋<12n2+ϵ n\sqrt{2}-\lfloor n\sqrt{2}\rfloor < \frac{1}{2n \sqrt{2}}+\epsilon.
functionfloor functionDiophantine equationalgebra unsolvedalgebra