How many five-digit numbers can be formed using digits $1,2,3,4,5,6$ which are divisible by $3$ and $5$?
128220
How many five-digit numbers can be formed using digits $0, 1, 2, 6, 7, 8,9$ which are divisible by $3$ and $5$?
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
117761
When is $\binom{n}{k}$ divisible by $n$?
35515
Find the number of $(m+n)$ digit binary sequences with $m$ $0$'s and $n$ $1$'s such that no two $1$'s are adjacent
143501
Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.
116970
On the number divisors of a number
105140
To find the total no. of six digit numbers that can be formed having property that every succeeding digit is greater than preceding digit.
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
43113
Whether the given number is divisible by 24?
137808
$n^2 + 3n +5$ is not divisible by $121$
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
102349
sum of all the numbers that can be formed using the digits 2,3,3,4,4,4..
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
134921
Find the number of all subsets of $\{1, 2, \ldots,2015\}$ with $n$ elements such that the sum of the elements in the subset is divisible by 5
117380
Divisibility Rule for 9
26857
In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.
42706
How many $N$ digits binary numbers can be formed where $0$ is not repeated