MathDB

672 numbers, what is the minimum of the largest one?

Source: Bulgaria JBMO TST 2018, Day 2, Problem 4

June 25, 2018

inequalities

Problem Statement

The real numbers

a_1 \leq a_2 \leq \cdots \leq a_{672}

are given such that

a_1 + a_2 + \cdots + a_{672} = 2018.

For any

n \leq 672

, there are

n

of these numbers with an integer sum. What is the smallest possible value of

a_{672}