MathDB

m in positive integer n such that f(n) = 2n, f(1992) = 2199, f(2000) = 200

Source: 1992 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p1

November 20, 2022

number theoryDigits

Problem Statement

Below the standard representation of a positive integer

n

is the representation understood by

n

in the decimal system, where the first digit is different from

0

. Everyone positive integer n is now assigned a number

f(n)

by using the standard representation of

n

last digit is placed before the first. Examples:

f(1992) = 2199

f(2000) = 200

. Determine the smallest positive integer

n

for which

f(n) = 2n

holds.