KöMaL 2012 A567

($a$) Find all pairs ($a$,$b$) of relatively prime positive integers $a$, $b$ such that $b$ divides $a^2$-3 and $a$ divides $b^2$-3. ($b$) Find all pairs ($a$,$b$) of relatively prime positive integers $a$, $b$ such that $b$ divides $a^2$-5 and $a$divides $b^2$-5.