What are the most interesting examples of unsolved problems in number theory which an 18 year can understand?
The Goldbach Conjecture is easy enough to understand: every even number greater than 2 is the sum of two prime numbers. Easy to state, fiendishly difficult to prove.
A lot are referenced in the book : "Unsolved problems in number theory", R.K.Gay, Springer Edit. Much of them are easy to understand.