Some basic math olympiad problems:
Divisible by 289?
For how many integers x, x^2 - 3x - 19 is divisible by 289?
For how many positive integral values of n, the expression n(4n + 1) is a perfect square?
Update (23/01/10)(05/02/10): Solution: Posted by Aaditya Ramdas (CSE IITB Alumnus & Tower Research), Piyush Sao (Senior Undergrad, EE, IITM) and Nikhil Garg (Sophomore, IITD) in comments!! Thanx.