IMO BinomialExpansion SpecialSequence
Challenging

Problem - 2698
Let $\{a_n\}$ be a sequence defined as $a_n=\lfloor{n\sqrt{2}}\rfloor$ where $\lfloor{x}\rfloor$ indicates the largest integer not exceeding $x$. Show that this sequence has infinitely many square numbers.
The solution for this problem is available for $0.99. You can also purchase a pass for all available solutions for $99.