What are the last two digits of 2^(2^2003)?
Is there an efficient way to work out how many factors a large number has?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Start working out the multiplication in reverse......
What do you know about the last digit if the answer ends in a 7?