1

Part of 2008 Spain Mathematical Olympiad

Problems(2)

Arithmetic mean of the divisors of n is an integer.

Source:

p

q

be two different prime numbers. Prove that there are two positive integers,

a

b

, such that the arithmetic mean of the divisors of

n=p^aq^b

number theory proposednumber theory

Find (a,b) if given a+b and lcm(a,b)

Source:

Find two positive integers

a

b

, when their sum and their least common multiple is given. Find the numbers when the sum is

3972

and the least common multiple is

985928

number theoryleast common multiplenumber theory proposed