$n^2+(n+1)^2+n^2\cdot(n+1)^2$ is a perfect square
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
59782
Are there any $n$ for which $ n^4+n^3+n^2+n+1$ is a perfect square?
38498
Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square
130499
How can $p^{q+1}+q^{p+1}$ be a perfect square?
55206
Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square
9146
Proving that a list of perfect square numbers is complete
106716
The sum of square roots of non-perfect squares is never integer
118538
Find all integers $x$ such that $x^2+3x+24$ is a perfect square.
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
44790
Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
71534
Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
27387
Show that $a+b+c=0$ implies that $32(a^4+b^4+c^4)$ is a perfect square.
54355
$1+x+\ldots+x^n$ perfect square
48787
A number is a perfect square if and only if it has odd number of positive divisors