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

Source: 1998 Estonia National Olympiad Final Round grade 11 p4

March 11, 2020
floor functionnumber theoryalgebrairrational

Problem Statement

A real number aa satisfies the equality 1a=a−[a]\frac{1}{a} = a - [a]. Prove that aa is irrational.
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