MathDB

Prove that there exists a function [Iran Second Round 1994]

Source:

November 26, 2010

functionpigeonhole principlemodular arithmeticnumber theory proposednumber theory

Problem Statement

Let

\overline{a_1a_2a_3\ldots a_n}

be the representation of a

n-

digits number in base

10.

Prove that there exists a one-to-one function like

f : \{0, 1, 2, 3, \ldots, 9\} \to \{0, 1, 2, 3, \ldots, 9\}

such that

f(a_1) \neq 0

and the number

\overline{ f(a_1)f(a_2)f(a_3) \ldots f(a_n) }

is divisible by

3.