Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
568
Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$.
48908
Choose 100 numbers from 1~200 (one less than 16) - prove one is divisible by another!
139935
Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10
129163
Showing that every positive integer can be represented in this form
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
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
21820
How to prove that a set is invariant?
118036
Proving at least 99 pairwise sums of the reals are non-negative
72402
Summation of natural number set with power of $m$
3632
Basic number theory proofs
30136
Proof that a Combination is an integer
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
145889
Prove if $56x = 65y$ then $x + y$ is divisible by $11$
17510
Proving a set is an abelian group.
17194
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
142008
Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
141895
Proving that a sequence is monotone