parmenides51 wrote: Let $n$ be a positive integer. Prove that there are no positive integers $x$ and $y$ such as $\sqrt{n}+\sqrt{n+1} < \sqrt{x}+\sqrt{y} <\sqrt{4n+2}$ https://artofproblemsolving.com/community/c6h1468822p8515444 https://math.stackexchange.com/questions/2386549/inequality-sqrtn-sqrtn1-sqrtx-sqrty-sqrt4n2?noredirect=1