olymmath

Putnam 2001 A1

  • Session A

Consider a set SS and a binary operation ∗*, i.e., for each a,b∈Sa,b\in S, a∗b∈Sa*b\in S. Assume (a∗b)∗a=b(a*b)*a=b for all a,b∈Sa,b\in S. Prove that a∗(b∗a)=ba*(b*a)=b for all a,b∈Sa,b\in S.

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, 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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