Let $n$ be a positive integer. If $2+2\sqrt{28n^2+1}$ is an integer, then it is a perfect square.
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
101162
Square root of $2$ is irrational
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
134765
Is an integer a sum of two rational squares iff it is a sum of two integer squares?
63383
Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square
121036
Is there any perfect squares that are also binomial coefficients?
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"
84220
Questions on perfect squares
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
130499
How can $p^{q+1}+q^{p+1}$ be a perfect square?
152754
When is the sum of divisors a perfect square?
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
44790
Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
38018
Arrangement of integers in a row such that the sum of every two adjacent numbers is a perfect square.