MathDB
Proof of Existence of n

Source: 2008 Japan Mathematical Olympiad Finals Problem 5

February 12, 2008
inductioninequalitiesirrational numbernumber theory proposednumber theory

Problem Statement

Can it be existed postive integers n n such that there are integers b b and non zero integers a_i\ (i\equal{}1,\ 2,\ \cdots n) for rational numbers r r which satisfies r\equal{}b\plus{}\sum_{i\equal{}1}^n \frac{1}{a_i}?