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