Find all real numbers $x$ such that $$x^3 = \{(x + 1)^3\}$$where $\{y\}$ denotes the fractional part of $y$, i.e. the difference between $y$ and the largest integer less than or equal to $y$.
Source: New Zealand NZMOC Camp Selection Problems 2012 Seniors 1
Tags: algebra
Find all real numbers $x$ such that $$x^3 = \{(x + 1)^3\}$$where $\{y\}$ denotes the fractional part of $y$, i.e. the difference between $y$ and the largest integer less than or equal to $y$.