if $a,b$ are natural numbers such that $(1+ab)|(a^2+b^2).$ then $\frac{a^2+b^2}{1+ab}$ is perfect square
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
138548
For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
68389
Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$
147848
Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square.
72437
Sum of the digits of a perfect square
67968
When is $2^n -7$ a perfect square?
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
48787
A number is a perfect square if and only if it has odd number of positive divisors
83248
Vieta Jumping: Related to IMO problem 6, 1988: If $ab + 1$ divides $a^2 + b^2$ then $ab + 1$ cannot be a perfect square.
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
147666
How to prove that either $2^{500} + 15$ or $2^{500} + 16$ isn't a perfect square?
134121
Determining all the positive integers $n$ such that $n^4+n^3+n^2+n+1$ is a perfect square.
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.