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\(\renewcommand{\d}{\displaystyle}\newcommand{\N}{\mathbb N}\newcommand{\st}{:}\)

Find the least element of each of the following sets, if there is one.

$\{n \in \N \st n^2 - 3 \ge 2\}\text{.}$

$\{n \ge 0 \st n^2 - 5 \in \N\}\text{.}$

$\{n^2+1 \st n \in \N\}\text{.}$

$\{n \in \N \st n = k^2 + 1 \text{ for some } k \in \N\}\text{.}$

If there is no least element, enter “none”.

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