Divisibility of 111...1111
Source: Asked to Russian 7th Graders - Taken from Wild For Math Blog
Is it true that among the numbers consisting of only "1"s (1; 11; 111; 1111; etc.) there is a number (maybe many) that is divisible by 572,003?
Here 572,003 is taken arbitrarily. Is it true for all numbers?
Update (November 02, 2011):
Solution posted in comments by NG a.k.a Nikhil Garg (IITD CSE Senior Undergraduate), Rudradev Basak (IITD CSE Senior Undergraduate, IMO Bronze Medalist), Yashoteja Prabhu (RA at Microsoft Research, IITB CSE 2011 Alumnus), Siva, Garvit Juniwal (IITB CSE Senior Undergraduate)! Thanks