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5.E: Temas adicionales (Ejercicios)
https://espanol.libretexts.org/Matematicas/Combinatoria_y_Matematicas_Discretas/Matem%C3%A1ticas_Discretas_(Levin)/5%3A_Temas_adicionales/5.E%3A_Temas_adicionales_(Ejercicios)
Asumir $a \mid b$ and $a \mid c\text{.}$ This means that $b$ and $c$ are both multiples of $a\text{,}$ so $b = am$ and $c = an$ for integers $m$ and $n\text{.}$ Then \(b+c = am+an = a...Asumir $a \mid b$ and $a \mid c\text{.}$ This means that $b$ and $c$ are both multiples of $a\text{,}$ so $b = am$ and $c = an$ for integers $m$ and $n\text{.}$ Then $b+c = am+an = a(m+n)\text{,}$ so $b+c$ is a multiple of $a\text{,}$ or equivalently, $a \mid b+c\text{.}$ Similarly, $b-c = am-an = a(m-n)\text{,}$ so $b-c$ is a multiple of $a\text{,}$ which is to say $a \mid b-c\text{.}$

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