Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4720. (May 2015)

B. 4720. Let $\displaystyle a$ and $\displaystyle n$ denote positive integers such that $\displaystyle a^n-1$ is divisible by $\displaystyle n$. Prove that the numbers $\displaystyle a+1$, $\displaystyle a^2+2$, ..., $\displaystyle a^n+n$ all leave different remainders when divided by $\displaystyle n$.

(6 pont)

Deadline expired on June 10, 2015.

### Statistics:

 16 students sent a solution. 6 points: Baran Zsuzsanna, Fekete Panna, Gál Boglárka, Gáspár Attila, Lajkó Kálmán, Nagy-György Pál, Németh 123 Balázs, Szebellédi Márton, Williams Kada. 5 points: Glasznova Maja. 4 points: 1 student. 3 points: 1 student. 1 point: 2 students. 0 point: 2 students.

Problems in Mathematics of KöMaL, May 2015