Find all positive integers n such that 20n+2 can divide 2003n+2002
48622
Given an integer $a$, suppose $d=\gcd(3a+5,\,5a+7)>2$. Determine $d$.
95409
Find no. of non negative integer solutions of $a+2b+3c = 200$
25338
Sum of $n$ integers from set of size $2n-1$ divides $n$
110958
How to solve for any given natural number n?
11470
Divisibility of integers
48655
Find all n such that : $3 \mid (n2^{n}+1)$
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.
77547
Find integers $a,b,c,d$ such that
62933
Determine a determinant is divisible by 23 or not
149489
30 positive integers
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
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
108504
Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
51211
Mathematics induction (exponential divisible by 2304)
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$