For no positive integer $n$ can both $n+3$ and $n^2 + 3n + 3$ be perfect cubes.
65965
Theoretical way to prove no positive integer $n$ exists such that $n+3$ and $n^2+3n+3$ are both perfect cubes.
98443
Find positive integers such that $2n^3 + 5|n^4 +n+1$
82636
Maybe is right $\frac{n^2 + 1}{4k + 3} \notin \mathbb{Z}, n, k \in \mathbb{N}^{+}$
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
23301
There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
60738
If 4n+1 and 3n+1 are both perfect sqares, then 56|n. How can I prove this?
100913
It is impossible for $(x-1)^2+x^2+(x+1)^2$ to be a perfect square
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
67356
When is $2^x+3^y$ a perfect square?
27984
Square matrices satisfying certain relations must have dimension divisible by $3$
45356
Are there any positive integers $a, b, c, d$ such that both $(a, b, c)$ and $(b, c, d)$ are Pythagorean triples?
87666
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
147848
Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square.
80229
How to prove this curiosity that has to do with cubes of certain numbers?
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
46102
Prove that $2^n +1$ in never a perfect cube
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.