A row of $2n$ real numbers is called “Sozopolian”, if for each $m$, such that $1\leq m\leq 2n$, the sum of the first $m$ members of the row is an integer or the sum of the last $m$ members of the row is an integer. What’s the least number of integers that a Sozopolian row can have, if the number of its members is: a) 2016; b) 2017?
Problem
Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade
Tags: number theory