Pigeonhole proof of the existence of two numbers with given sum
94923
Using the Pigeonhole Principle to show that $2$ of any $n+1$ numbers from $\{1,2,\ldots,2n\}$ sum to $2n+1$
72591
Find a bijection to prove a fact about integer partitions
94209
Prove by contradiction that every integer greater than 11 is a sum of two composite numbers
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
7785
Cardinality of sum-set
31744
Proving that there is an irrational number between any two unequal rational numbers.
50615
Expressing a Non Negative Integer as Sums of Two Squares
40080
Sum of multiples of $2$ coprime numbers cover positive integers
81567
Pigeon hole principle to prove $a-b=9$ in subset.
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
138081
How to determine whether a number can be written as a sum of two squares?
78163
Hint for problem on $4 \times 7$-chessboard problem related to pigeonhole principle
33104
Combinatorial Proof with Summation Identity
152333
A problem based on pigeonhole
75852
Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other
4194
Which integers can be expressed as a sum of squares of two coprime integers?
103347
combinatorial proof of summation