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image of floor function

Source: 1998 France MO P3

April 10, 2021
floor functionalgebrafunction

Problem Statement

Let k≥2k\ge2 be an integer. The function f:N→Nf:\mathbb N\to\mathbb N is defined by f(n)=n+⌊n+nkk⌋.f(n)=n+\left\lfloor\sqrt[k]{n+\sqrt[k]n}\right\rfloor.Determine the set of values taken by the function ff.
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