For too long, the problems on this website have been an endless bore of routine homework quesitons/calculations. Here is a question to provoke some thought:

For all \(x\) such that \(\{x\}+\frac1x=1\), is it necessarily true that \(\{x^n\}+\frac1{x^n}=1\) for all nonnegative \(n\)? Here \(\{x\}\) denotes the fractional part of \(x\).

Guest Jul 22, 2023