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6x6 system, a = max {1/b, 1/c}

Source: Switzerland - 2007 Swiss MO Final Round p1

December 26, 2022
algebrasystem of equationsSysteminequalities

Problem Statement

Determine all positive real solutions of the following system of equations: a= max{1b,1c}      b=max⁡{1c,1d}      c=max⁡{1d,1e}a =\ max \{ \frac{1}{b} , \frac{1}{c}\} \,\,\,\,\,\, b = \max \{ \frac{1}{c} , \frac{1}{d}\} \,\,\,\,\,\, c = \max \{ \frac{1}{d}, \frac{1}{e}\} d=max⁡{1e,1f}      e=max⁡{1f,1a}      f=max⁡{1a,1b}d = \max \{ \frac{1}{e} , \frac{1}{f }\} \,\,\,\,\,\, e = \max \{ \frac{1}{f} , \frac{1}{a}\} \,\,\,\,\,\, f = \max \{ \frac{1}{a} , \frac{1}{b}\}
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