Find the remainder when 3^{2013} is divided by 13.

Number | Remainder when divided by 13 |

3^{1} |
3 |

3^{2} |
9 |

3^{3} |
1 |

3^{4} |
3 |

3^{5} |
9 |

3^{6} |
1 |

3^{7} |
3 |

3^{8} |
9 |

3^{9} |
1 |

. | . |

. | . |

. | . |

3^{2013} |
? |

When successive powers of 3 are divided by 13, a pattern emerges. Since 2013 is a multiple of 3, the remainder when 3^{2013} is divided by 13 is 1.

(Note: You can adapt this to any power of 3 your students might like.)