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x

prove that:\r\n\r\n x\\in \\mathbb{Z}\\Leftrightarrow \\lfloor x\\rfloor \\plus{}\\lfloor 2x\\rfloor\\plus{}\\lfloor 3x\\rfloor\\plus{}...\\plus{}\\lfloor nx\\rfloor\\equal{}\\frac{n(\\lfloor x\\rfloor\\plus{}\\lfloor nx\\rfloor)}{2}\\ ,\\ (\\forall)n\\in \\mathbb{N}^*"}}]}]}]]}],"$L26"]}]]}]