Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 661. (January 2016)

A. 661. Let $\displaystyle K$ be a fixed positive integer. Let $\displaystyle (a_0,a_1,\dots)$ be the sequence of real numbers that satisfies $\displaystyle a_0=-1$ and

$\displaystyle \sum_{\substack{i_0,i_1,\dots,i_K\ge0 \\ i_0+i_1+\dots+i_K=n}} \frac{a_{i_1}\cdot\dots\cdot a_{i_K}}{i_0+1} =0$

for every positive integer $\displaystyle n$. Show that $\displaystyle a_n>0$ for $\displaystyle n\ge1$.

(5 pont)

Deadline expired on February 10, 2016.

### Statistics:

 1 student sent a solution. 5 points: Williams Kada.

Problems in Mathematics of KöMaL, January 2016