Prove exists consecutive integers $s,s+1,\dots,s+i$ such that $m_{i}|s+i$, if $m_{0},\dots,m_{r}$ are positive integers coprime
59535
Prove that there exists such a set of $n$ positive integers
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
60615
Product of $5$ consecutive integers cannot be perfect square
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
139350
Given two coprime integers, find multiples of them that differ by 1
129163
Showing that every positive integer can be represented in this form
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
20438
Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
113248
Proving $r!$ divides the product of r succesive positive integers
77128
Necessary and Sufficient conditions for $(i \, j)$ and $(1 \, 2 \, \dotsc \, n)$ generate $S_n$.
63240
Every two consecutive integers are coprime.
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
131476
consecutive prime power
94575
Inductive proof that there are infinitely many pairs of consecutive powerful integers?
77200
Prove:that in any set of 1009 positive integers exits two numbers $a_i$ and $a_j$ such that $a_i-a_j$ or $a_i+a_j$ is divisible by 2014
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$