MathDB

5

Part of 2013 Romanian Master of Mathematics

Problems(1)

RMM 2013 Problem 5

Source:

3/3/2013
Given a positive integer k≥2k\geq2, set a1=1a_1=1 and, for every integer n≥2n\geq 2, let ana_n be the smallest solution of equation x=1+∑i=1n−1⌊xaik⌋x=1+\sum_{i=1}^{n-1}\left\lfloor\sqrt[k]{\frac{x}{a_i}}\right\rfloor that exceeds an−1a_{n-1}. Prove that all primes are among the terms of the sequence a1,a2,…a_1,a_2,\ldots
floor functioninductionnumber theory