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Found problems: 1

2004 Nicolae Coculescu, 3
Tags: equation , hermite , floor , fractional , algebra
Prove the identity $ \frac{n-1}{2}=\sum_{k=1}^n \left\{ \frac{m+k-1}{n} \right\} , $ where $ n\ge 2, m $ are natural numbers, and $ \{\} $ denotes the fractional part.