IMO EulerFermatTheorem LinearRecursion
Challenging

Problem - 2699

Let sequence $g(n)$ satisfy $g(1)=0, g(2)=1, g(n+2)=g(n+1)+g(n)+1$ where $n\ge 1$. Show that if $n$ is a prime greater than 5, then $n\mid g(n)[g(n)+1]$.

The solution for this problem is available for $0.99. You can also purchase a pass for all available solutions for $99.