Problem #PRU-111805

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

Problem

The sequence \((a_n)\) is given by the conditions \(a_1 = 1000000\), \(a_{n + 1} = n \lfloor a_n/n\rfloor + n\). Prove that an infinite subsequence can be found within it, which is an arithmetic progression.