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Found problems: 1

2010 Laurențiu Panaitopol, Tulcea, 2
Tags: algebra , function , floor function , quadratic integers
Let be a nonnegative integer $ n $ such that $ \sqrt n $ is not integer. Show that the function $$ f:\{ a+b\sqrt n | a,b\in\{ 0\}\cup\mathbb{N} , a^2-nb^2=1 \}\longrightarrow\{ 0\}\cup\mathbb{N} , f(x) =\lfloor x \rfloor $$ is injective and non-surjective.