When is $8^n b^n + \cdots + 8 b + 1$ a perfect square (for positive integer $b$)?
54355
$1+x+\ldots+x^n$ perfect square
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
106716
The sum of square roots of non-perfect squares is never integer
99606
Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
5692
Proving that there is a perfect square between $n$ and $2n$
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
41641
$(n-7)(n+7)=$ some perfect square
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
152643
$(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
9146
Proving that a list of perfect square numbers is complete
131108
Can $3p^4-3p^2+1$ be square number?
74898
$1^n +2^n + \cdots +(p-1)^n \mod p =$?
21906
Show $3^m + 3^n +1$ cannot be a perfect square for $m,n$ being positive integers.
38498
Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square
114404
For which positive integer values of $n$ does $a|mn-b?$