State all solutions (a,b,c) for the system of equations a+b+c=2009 and log_a(b) = c^2009 where a,b,c are integers and a >= 2, b>= 1, c>=0. Explain your answer. Hint: First consider c.

hint doesn't really help me tbh.. just trying to solve some problems from last year's test and this is the only one i'm stuck on. any help regarding the approach would be appreciated