MathDB
RMM 2013 Problem 5

Source:

March 3, 2013
floor functioninductionnumber theory

Problem Statement

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
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