In any set of ten consecutive positive integers, there is one that is coprime with each one of the others
47960
Given any $10$ consecutive positive integers , does there exist one integer which is relatively prime to the product of the rest ?
136964
Prove there exist 135 consecutive integers that each have a perfect cube $>1$ that divides it.
105985
Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers
58103
number of permutations in which no two consecutive numbers are adjacent
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
17786
Existence of Consecutive Quadratic residues
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
104527
Prove that there are two subsets of any cardinality-10 subsets of $\{1,2\dots,106\}$ that sum to the same number
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
40080
Sum of multiples of $2$ coprime numbers cover positive integers
40635
Finding Maximum value of consecutive positive integers with constraints
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
39563
How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
144575
Factoring n, where n=pq and p and q are consecutive primes