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 Tow Problems
06-01-2010, 10:52 PM
Post: #1
 elim Moderator Posts: 580 Joined: Feb 2010 Reputation: 0
Tow Problems
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 -
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