Question 140
Let $a$ and $n$ be two nonzero natural numbers such that
$$
\{\sqrt{n+\sqrt{n}}\}=\{\sqrt{a}\}
$$
(where $\{x\}$ denotes the fractional part of $x$). Show that $4a+1$ is a perfect square.
$$
\{\sqrt{n+\sqrt{n}}\}=\{\sqrt{a}\}
$$
(where $\{x\}$ denotes the fractional part of $x$). Show that $4a+1$ is a perfect square.