Show that sequence of composition of function $f(n) = n + \lfloor{\sqrt{n}}\rfloor$ contains at least one perfect square.
134
Prove that the expression is a perfect square
9146
Proving that a list of perfect square numbers is complete
5692
Proving that there is a perfect square between $n$ and $2n$
146023
How to prove that $x^2 - \lfloor x\rfloor^2$ is onto?
52157
Prove that $d(n)\leq 2\sqrt{n}$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
106960
Proof to sequences in real analysis
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
19588
$n!+1$ being a perfect square
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
143642
Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
55826
Convergence of sequence of real numbers and (sub)subsequence
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.