Solution

Problem 1 http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2597742&sid=f8eee982acf0b5b25d85297a0b62a709#p2597742

Problem 2 http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2597733&sid=f8eee982acf0b5b25d85297a0b62a709#p2597733

Problem 3 http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2597744&sid=f8eee982acf0b5b25d85297a0b62a709#p2597744

Problem 4 http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2597923&sid=f8eee982acf0b5b25d85297a0b62a709#p2597923