Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 700. (May 2017)

A. 700. A positive integer $\displaystyle n$ satisfies the following: it is possible to select some integers such that if we randomly choose two different integers from this list, say, $\displaystyle i$ and $\displaystyle j$, then $\displaystyle i+j$ $\displaystyle \mathrm{mod\ } n$ is equal to one of the numbers $\displaystyle 0,1,\dots,n-1$ with equal probability. Find all numbers $\displaystyle n$ with this property.

(5 pont)

Deadline expired on June 12, 2017.

### Statistics:

 7 students sent a solution. 5 points: Baran Zsuzsanna, Gáspár Attila, Matolcsi Dávid, Williams Kada. 4 points: Szabó Kristóf. 0 point: 2 students.

Problems in Mathematics of KöMaL, May 2017