4

Part of 2010 Middle European Mathematical Olympiad

Problems(1)

MEMO 2010, Problem I-4: Difference of divisors divides n

Source:

Find all positive integers

n

which satisfy the following tow conditions: (a)

n

has at least four different positive divisors; (b) for any divisors

a

b

n

1<a<b<n

b-a

n

.
(4th Middle European Mathematical Olympiad, Individual Competition, Problem 4)

inequalitiesnumber theory proposednumber theoryeasy problem