MathDB

s(k)+s(f(n)-k) = n, sum of digits

Source: 1997 Swedish Mathematical Competition p5

April 2, 2021

number theorysum of digits

Problem Statement

Let

s(m)

denote the sum of (decimal) digits of a positive integer

m

. Prove that for every integer

n > 1

not equal to

10

there is a unique integer

f(n) \ge 2

such that

s(k)+s(f(n)-k) = n

for all integers

k

with

0 < k < f(n)