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Found problems: 1

2006 Cezar Ivănescu, 2
Tags: albegra , fractional part , number theory , algebra
[b]a)[/b] Prove that $ \{ a \} +\{ 1/a \} <3/2, $ for any positive real number $ a. $ [b]b)[/b] Give an example of a number $ b $ satisfying $ \{ b \} +\{ 1/b \} =1. $ [i]{} means fractional part[/i]