Showing that in a given set of 7 distinct integers that there must be at least one pair in the set whose sum or difference is a multiple of 10.
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
146867
Combinatorial Proof Of A Number Theory Theorem--Confusion
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
27889
If the set of odd numbers is a subset of $\mathbb N$ then surely it is smaller than $\mathbb N$
24954
Prove that there are infinitely many integers of the form $111\ldots111$ that are multiple of $n$.
156577
The cube of any number not a multiple of $7$, will equal one more or one less than a multiple of $7$
83518
Proving Two sets have same cardinality
118036
Proving at least 99 pairwise sums of the reals are non-negative
53937
Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$.
125040
Show by induction : $n^7-n$ is a multiple of 7
30136
Proof that a Combination is an integer
150324
Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
1409
Proving that the given set has at most $2^{n-1}$ elements
124667
Let $S=\{3,4,5,6,7,8,9,10,11,12\}$. Suppose 6 integers are chosen from S. Must there be 2 integers whose sum is 15?
103538
Partitions of $n$ into distinct odd and even parts proof
144821
Number of ordered pairs of subsets
92737
primes whose difference is a multiple of $n$