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