Chapter 5, Problem 28RE

(a)

To determine

To prove: That $n{\tau }^2-n\tau$ is an integer where $\tau =\frac{1+\sqrt{5}}{2}$ denote the golden mean and $n\ge 1$.

(b)

To determine

That $\lfloor n{\tau }^2\rfloor -\lfloor n\tau \rfloor =n$ where $\tau =\frac{1+\sqrt{5}}{2}$ denote the golden mean and $\lfloor \rfloor :R\to Z$ the usual floor function. Also, $n\ge 1$.