Mathematical and Physical Journal
for High Schools
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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.


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