Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

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