To find positive integers $n$ such that $\dfrac {n(n+1)(n+2)}6$ is a perfect square
121036
Is there any perfect squares that are also binomial coefficients?
114404
For which positive integer values of $n$ does $a|mn-b?$
43865
Find all positive integers $n$ such that $\phi(n)=6$.
114542
Can a number with $100$ $0$'s $100$ $1$'s and $100$ $2$'s ever be a perfect square?
10920
$\delta_2(n)$ the sum of the squares of the positive divisors of $n$.
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
99606
Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
152754
When is the sum of divisors a perfect square?
91451
find all positive integer $m,n$
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
90076
Prove that every positive integer $n$ is a unique product of a square and a squarefree number
67968
When is $2^n -7$ a perfect square?
59535
Prove that there exists such a set of $n$ positive integers
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.