MathDB
Math Prize 2011 Problem 19

Source:

September 19, 2011

Problem Statement

If 1<x<1-1 < x < 1 and 1<y<1-1 < y < 1, define the "relativistic sum'' xyx \oplus y to be xy=x+y1+xy. x \oplus y = \frac{x + y}{1 + xy} \, . The operation \oplus is commutative and associative. Let vv be the number v=1771177+1. v = \frac{\sqrt[7]{17} - 1}{\sqrt[7]{17} + 1} \, . What is the value of vvvvvvvvvvvvvv? v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \oplus v \, ? (In this expression, \oplus appears 13 times.)