Remove any number and the remaining numbers can be partitioned into two subsets of equal sum; prove all numbers are equal.
65780
After removing any part the rest can be split evenly. Consequences?
74713
Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
41571
Prove that in a sequence of numbers $49 , 4489 , 444889 , 44448889\ldots$
66948
Proving question on sets
31890
Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.
120309
Number Theory Inequality Proof
72591
Find a bijection to prove a fact about integer partitions
113083
How to prove a set equality?
43979
The total number of subsets is $2^n$ for $n$ elements
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges
104527
Prove that there are two subsets of any cardinality-10 subsets of $\{1,2\dots,106\}$ that sum to the same number
150324
Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
76405
Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}
28496
Generating the partitions of a number
94209
Prove by contradiction that every integer greater than 11 is a sum of two composite numbers