Problem 1

Part of 2003 Spain Mathematical Olympiad

Problems(1)

2003 National Spain Olympiad, Problem 1

Source: 2003 National Spain Olympiad

Prove that for any prime

{p}

, different than

{2}

{5}

, there exists such a multiple of

{p}

whose digits are all nines. For example, if

{p = 13}

, such a multiple is

{999999 = 13 * 76923}

number theoryprime numbers