Prove that $a+b$ is a perfect square
67528
"If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer"
19588
$n!+1$ being a perfect square
100913
It is impossible for $(x-1)^2+x^2+(x+1)^2$ to be a perfect square
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
112368
Is there a rule for $\sqrt{a+b}$?
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
91285
Prove $a+b+c+d $ is composite
48430
Prove the following sequence always results in a perfect square.
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
145558
Prove that $2^n+3^n $ is never a perfect square
54355
$1+x+\ldots+x^n$ perfect square
84220
Questions on perfect squares
152643
$(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is