Exercise 2.3.4 (First examples, part 4)

Question

Find all integers that give the remainders $1,2,3$ when divided by $3,4,5$ respectively.

Richard Ganaye · Accepted Answer

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

\begin{proof} An integer $x$ is a solution if
$$x \equiv 1 \pmod 3,\qquad x \equiv 2 \pmod 4, \qquad x \equiv 3 \pmod 5,$$
where $3,4,5$ are relatively prime by pairs.

A solution is $x_0 = -2$, so the solutions are
$$x = -2 + k 60,\ k\in \Z.$$
\end{proof}

Exercise 2.3.4 (First examples, part 4)

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Exercise 2.3.4 (First examples, part 4)

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