MathDB

Sum of divisors

Source: St Petersburg Olympiad 2011, Grade 10, P2

September 15, 2017

number theory

Problem Statement

n

- some natural. We write on the board all such numbers

d

, that

d\leq 1000

and

d|n+k

for some

1\leq k \leq 1000

. Let

S(n)

-sum of all written numbers. Prove , that

S(n)<10^6

and

S(n)>10^6

has infinitely many solutions.