Question: If $a N = \{ a x : x \in N \}$ and $c \in N$ are relatively prime, then...

Question

If $a N = \{ a x : x \in N \}$ and $c \in N$ are relatively prime, then

Answer 1

$b N =$ the set of positive integral multiples of b, $c N$ = the set of positive integral multiplies of c.

$\therefore$ $b N \cap c N$ = the set of positive integral multiples of bc

= $\because b , c$ are prime]

$\therefore$ $d = b c$ .

Question: If \(a N = \{ a x : x \in N \}\) and \(c \in N\) are relatively prime, then...