Exercise 2.1.5 (First examples, part 5)

Question

Write a single congruence that is equivalent to the pair of congruences

$x\equiv 1 \pmod 4, x \equiv 2 \pmod 3$.

Richard Ganaye · Accepted Answer

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

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

\begin{proof} 
Since $\mathrm{gcd}(4,3) = 1$,
$$
\left\{
\begin{array}{ll}
x\equiv 1 &\pmod 4\
x \equiv 2 &\pmod 3
\end{array}
ight.
\iff 
\left\{
\begin{array}{ll}
x\equiv 5 &\pmod 4\
x \equiv 5 &\pmod 3
\end{array}
ight.
\iff
x \equiv 5 \pmod {12}.
$$

Exercise 2.1.5 (First examples, part 5)

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Exercise 2.1.5 (First examples, part 5)

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