prove that there exists a perfect cube that divides 135 consecutive integers
136964
Prove there exist 135 consecutive integers that each have a perfect cube $>1$ that divides it.
131476
consecutive prime power
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
153769
Numbers that can be expressed as the sum of two cubes in exactly two different ways
101832
Proof that sum of first $n$ cubes is always a perfect square
44528
The only natural number $x$ for which $x+\sqrt{-2}$ is a cube in $\mathbb{Z}[\sqrt{-2}]$ is $x=5$
59535
Prove that there exists such a set of $n$ positive integers
128716
Intuitive/direct proof that a rectangle partitioned into rectangles each with at least one integer side must itself have an integer side
53937
Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$.
80229
How to prove this curiosity that has to do with cubes of certain numbers?
40635
Finding Maximum value of consecutive positive integers with constraints
5692
Proving that there is a perfect square between $n$ and $2n$
68882
Path to Combinatorics Problem [$1.11$]
63383
Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square
87666
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
139935
Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10
93657
Proving “The sum of $n$ consecutive cubes is equal to the square of the sum of the first $n$ numbers.”