[ [Properties of numbers. General properties ]  $[$ Evenness and oddness $\quad]$

Author: frankkin 5. . $\quad$.

All natural numbers from 1 to 1000 are arranged in a circle in some order such that each number is a divisor of the sum of its two neighbors. It is known that next to the number $k$ are two odd numbers. What parity can the number $k$ have? 

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Note that two even numbers cannot stand next to each other, because then the number following them would also be even, and so on, meaning all numbers on the circle would end up being even. Since there are exactly half as many even numbers, they alternate with odd numbers, hence $k$ is even.

## Answer

Even.