Problem 559

Let $\lfloor x\rfloor$ be the greatest integer not exceeding $x$. For instance, $\lfloor 3.4\rfloor=3,\lfloor 2\rfloor=2$, and $\lfloor-2.7\rfloor=-3$. Determine the value of the constant $\lambda>0$ so that $2\lfloor\lambda n\rfloor=1-n+\lfloor\lambda\lfloor\lambda n\rfloor\rfloor$ for all positive integers $n$.