Hi guys, international teams have just finished the first day of IMO (International Mathematics Olympiad). The first problem is about number theory, which is one of my interesting fields. It took me a while to think of a brief solution: 

 

Determine all composite integers n>1 that satisfy the following property: if d1,d2,..., dk, are all positive divisors of n with 1=d1<d2<d3<...<dk=n, then di divides d_(i+1)+d_(i+2) for every 0<i<k-1: