Tow Problems - Printable Version +- OMath! (http://math.elinkage.net) +-- Forum: Math Forums (/forumdisplay.php?fid=4) +--- Forum: Number Theory (/forumdisplay.php?fid=7) +--- Thread: Tow Problems (/showthread.php?tid=77) Tow Problems - elim - 06-01-2010 10:52 PM 1. Let $g(n)$ be the greatest odd divisor of $n$, show that $\mathop {\lim }\limits_{n \to + \infty } \frac{1} {n} \cdot \sum\limits_{k = 1}^n {\frac{{g\left( k \right)}} {k}}$ exists and find it ( Bulgaria 1985) 2. Find all $k \in \mathbb{Z}\text{ with }k \geq 2$ such that $n \not|g(k^n+1)$, $\forall n \in \mathbb{Z}, \quad (n>1)$ (Olimpíada Rioplatense 2008) - $g(n)$ is defined as in 1 -