Determine the number of positive integers such that $[\frac{a}{2}] + [\frac{a}{3}] + [\frac{a}{5}] = a$
113237
Find the sum of the roots of the floor equation
148796
Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
129163
Showing that every positive integer can be represented in this form
115284
For $5$ distinct integers $a_i$, $1\le i\le5$, $f(a_i)=2$. Find an integer b (if it exists) such that f(b) = $9$.
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
14815
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
85959
How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
20713
The sum of an uncountable number of positive numbers
21531
The number of nonnegative integer triples with sum equal to $12$
149489
30 positive integers
106030
Find all the positive integer
119278
The number $\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^n\right]$ is always an integer
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1