There exists a perfect square between $n$ and $2n$
5692
Proving that there is a perfect square between $n$ and $2n$
87666
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
154082
Product of factorials divided by factorial to produce perfect square
41641
$(n-7)(n+7)=$ some perfect square
19954
Perfect set without rational numbers
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
80458
How to efficiently find the largest perfect square dividing a given large integer?
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
138548
For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
152754
When is the sum of divisors a perfect square?
84220
Questions on perfect squares
149071
Let $d$ be any positive integer not equal to $2, 5,$ or $ 13$ , then $\exists a, b \in \{2, 5, 13, d\}$ such that $ab − 1$ is not a perfect square?
65965
Theoretical way to prove no positive integer $n$ exists such that $n+3$ and $n^2+3n+3$ are both perfect cubes.