olymmath

Putnam 2009 A4

  • Session A

Let SS be a set of rational numbers such that

(a) 0∈S0 \in S;

(b) If x∈Sx \in S then x+1∈Sx+1\in S and x−1∈Sx-1\in S; and

(c) If x∈Sx\in S and x∉{0,1}x\not\in\{0,1\}, then 1x(x−1)∈S\frac{1}{x(x-1)}\in S.

Must SS contain all rational numbers?

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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