MathDB

3

Part of 2005 Argentina National Olympiad

Problems(1)

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

Source: Argentina 2005 OMA L3 p3

5/12/2024
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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