Prove or disprove there always exists a set of four numbers of which product is a perfect square out of arbitrarily chosen $48$ positive integers ...
99606
Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
80671
Product of sums of square is a sum of squares.
114796
Direct proof that the product of odd integers is odd
14783
A Number Theory problem (GCD)
60284
Infinitely many positive integers $n$ such that $\phi(n) = \frac{n}{4}$?
121036
Is there any perfect squares that are also binomial coefficients?
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
114393
If $a$ is divisible by $4$, then there exist int $b$ and $c$ such that $a = b^2 - c^2$
42744
Prove a number is even using the Pigeonhole Principle
126015
Elementary number theory in sets
65965
Theoretical way to prove no positive integer $n$ exists such that $n+3$ and $n^2+3n+3$ are both perfect cubes.
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
39670
Use Pigeonhole to show of any set of $2^{n+1}-1$ positive integers is possible choose $2^{n}$ elements such that their sum is divisible by $2^{n}$.
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
129163
Showing that every positive integer can be represented in this form