olymmath

INMO 2009 Problem 3

  • Answer

Find all real numbers xx such that

[x2+2x]=[x]2+2[x]\left[x^{2}+2 x\right]=[x]^{2}+2[x]

(Here [x][x] denotes the largest integer not exceeding xx.)

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

{-1,-2,-3, \ldots} \cup\left{\cup_{n=-1}^{\infty}\left[n, \sqrt{1+(n+1)^{2}}-1\right)\right}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Locator in-inmo/2009/p3 · Tag XQYSNQBCGK · Edit this page on GitHub · Keys: j next, k previous