I'm stuck in proving this statement of division

Question

Can anyone help me prove if n divides a and n divides b, then n divides (ax + by).

I'm not sure if writing in the form of : a = nx and b = ny are still allowed to be used as x and y exists in the definition of the conclusion. I was thinking of using other variables such as: a = nc, and b = nd but I got stuck instead.

And so... if $a=nc$ and $b=nd$, then $ax+by = \dots$ where you make the replacements you suggested... — JMoravitz, Jan 22 '20 at 03:40
$\frac{a}{n}$ and $\frac{b}{n}$ then $\frac{ax}{n}+\frac{by}{n}$ — TheStudent, Jan 22 '20 at 03:41

score 0 · Answer 1 · answered Jan 22 '20 at 03:40

0

If $n$ divides $a$ then $a=nc$. If $n$ divides $b$ then $b=nd$.

So $ax+by=ncx+ndy=n(cx+dy)$, so $n $ divides $ax+by$.

answered Jan 22 '20 at 03:40

J. W. Tanner

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I'm stuck in proving this statement of division

1 Answers1