Let $a$ and $b$ be positive integers such that $ab + 1$ divides $a^2 + b^2$. Show that $(a^2 + b^2)/(ab + 1)$ is a perfect square.
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
134
Prove that the expression is a perfect square
67356
When is $2^x+3^y$ a perfect square?
113168
If $a > b$, is $a^2 > b^2$?
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
105564
If $n$ is a positive integer greater than 1 such that $3n+1$ is perfect square, then show that $n+1$ is the sum of three perfect squares.
48787
A number is a perfect square if and only if it has odd number of positive divisors
41641
$(n-7)(n+7)=$ some perfect square
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$