I have the following problem that I am struggling with. The problem is this:
Let $a,b,c$ be integers. Prove that if $ab+c = a^2c-b+a$ then $\gcd(a,c)=\gcd(b,c)$
I tried lots of rearranging of the above formula to get it into a form that resembles: $ax+cy = bi+cj$ which is $\gcd(a,c)=\gcd(b,c)$ by $\gcd$ characterization but have had little success.
Any help would be appreciated! Thanks!