Paragraph

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

1. \(\displaystyle \{n \in \N \st n^2 - 3 \ge 2\}\text{.}\)

2. \(\displaystyle \{n \in \N \st n^2 - 5 \in \N\}\text{.}\)

3. \(\displaystyle \{n^2+1 \st n \in \N\}\text{.}\)

4. \(\displaystyle \{n \in \N \st n = k^2 + 1 \text{ for some } k \in \N\}\text{.}\)