Prove that there are two numbers among them such that one divides the other
75852
Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other
74561
Let $a_1,a_2,\cdots,a_n$ be $n$ numbers such that $a_i$ is either $1$ or $-1$.If $a_1a_2a_3a_4+\cdots+a_na_1a_2a_3=0$ then prove that $4\mid n$.
118161
Proof of dividing fractional expressions
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
107335
Prove equality between binomial coefficients.
13739
For all $n>2$ there exists a prime number between $n$ and $ n!$
120309
Number Theory Inequality Proof
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
80365
Prove that $n$ is divisible by $6$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
152084
Binomial-Theorem proof
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
96169
$n$ divides a product of $n$ consecutive integers (by $n$ divides one of them)