Exercise 2.1.4 (First examples, part 4)

Question

If an integer $x$ is even, observe that it must satisfy the congruence $x \equiv 0 \pmod 2$. If an integer $y$ is odd, what congruence does it satisfy? What congruence does an integer $z$ of the form $6k+1$ satisfy?

Richard Ganaye · Accepted Answer

ewcommand{\Z}{\mathbb{Z}}

ewcommand{\N}{\mathbb{N}}

\begin{proof} 
\begin{align*}
y 	ext{ is odd } \iff & \exists k \in \Z,\ y = 2k +1  \iff y \equiv 1 \pmod 2.\
& \exists k \in \Z,\ z = 6k + 1 \iff z \equiv 1 \pmod 6.
\end{align*}
\end{proof}

Exercise 2.1.4 (First examples, part 4)

Answers

Comments

Exercise 2.1.4 (First examples, part 4)

Answers

Comments

Add answer