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a is irrational if 1/a=a-[a]

Source: Argentina 2005 OMA L3 p3

May 12, 2024
algebrafloor function

Problem Statement

Let aa be a real number such that 1a=a−[a]\frac{1}{a}=a-[a]. Show that aa is irrational.
Clarification: The brackets indicate the integer part of the number they enclose.
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