MathDB

Putnam 2009 A4

Source:

December 7, 2009

Putnaminductionmodular arithmeticgreatest common divisorquadraticscalculusintegration

Problem Statement

Let

S

be a set of rational numbers such that (a)

0\in S;

(b) If

x\in S

then x\plus{}1\in S and x\minus{}1\in S; and (c) If

x\in S

and

x\notin\{0,1\},

then \frac{1}{x(x\minus{}1)}\in S. Must

S

contain all rational numbers?