User:Popcrate/TWA/Earth

An integer n is even if, and only if, n equals twice some integer. An integer n is odd

if, and only if, n equals twice some integer plus 1.

Symbolically, if n is an integer, then

n is even ⇔ ∃ an integer k such that n = 2k.

n is odd ⇔ ∃ an integer k such that n = 2k + 1.

19.

Prove that for all integers n, n^2 − n + 3 is odd.

n2 − n + 3

$$\begin{array}{lcr} n^2 - n + 3 \\ n^2 - n + 2 + 1 \\ n^2 - n + 2 + 1

\end{array} $$