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TOT 086 1985 Spring J2 fractional part equation {A} +{1/A}=1

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August 24, 2019
floor functionInteger Partfractional part

Problem Statement

The integer part I(A)I (A) of a number AA is the greatest integer which is not greater than AA , while the fractional part F(A)F(A) is defined as Aāˆ’I(A)A - I(A) . (a) Give an example of a positive number AA such that F(A)+F(1/A)=1F(A) + F( 1/A) = 1 . (b) Can such an AA be a rational number?
(I. Varge, Romania)
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