Answer:
Let [tex](a,b)[/tex] denote the greatest common divisor of [tex]a\, \text{and}\, b[/tex]. We can prove this result as follows:
Step-by-step explanation:
The Bezout's identity establishes that [tex](a,c)=1[/tex] if and only if [tex]ax+cy=1[/tex] for some integers [tex]x,y[/tex].Since [tex]b\lvert c[/tex] then we have that [tex]c=bq[/tex] for some [tex]q\in \mathbb{Z}[/tex]. Then,
[tex]ax+cy=ax+(bq)y=ax+b(yq)=ax+bz=1[/tex]
Using the result of the Bezout's identity again we can concluide that [tex](a,b)=1[/tex].
