MathDB
Multiply by the next one - quartets

Source: 1961 All-Soviet Union Olympiad

August 4, 2015
combinatoricstransformationinvariant

Problem Statement

Consider a quartet of positive numbers (a,b,c,d)(a,b,c,d). In one step, we transform it to (ab,bc,cd,da)(ab,bc,cd,da). Prove that you can never obtain the initial set if neither of a,b,c,da,b,c,d is 11.
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