1. Let a, b, c, r, and t be integers. Prove that if a divides both b and c, then a divides br + ct.
2. Let b, c and d be integers. If b divides c and c divides d, then the equation bx = d has an integer solution. [Note: x is a variable.]
Thank you.
Abstract Algebra, I think, is way more complicated then Advanced Calculus. Because the nice thing about analysis is that it can be visualized that is what makes it simpler. With Algebra there is absolutely no visualization at all. I would also say that Abstract Algebra is as difficult as courses get.