MathDB
[a^m] + 1 is divisible by n

Source: VI Soros Olympiad 1990-00 R1 10.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
number theory

Problem Statement

Prove that for every integer n≥1n \ge 1 there exists a real number aa such that for any integer m≥1m \ge 1 the number [am]+1[a^m] + 1 is divisible by nn ([x][x] denotes the largest integer that does not exceed xx).
Back to ProblemsView on AoPS