MathDB
Bootstrapping an inequality at integer values

Source: Czech-Polish-Slovak Junior Match 2024, I-4

May 29, 2024
inequalitiesinequalities proposedInteger

Problem Statement

Let a,b,ca,b,c be integers satisfying a+b+c=1a+b+c=1 and ab+bc+ca<abcab+bc+ca<abc. Show that ab+bc+ca<2abcab+bc+ca<2abc.
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