Not so good with the number theory and don't understand #59 and #61 on the practice GRE. Not even really sure where to start with these problems.(adsbygoogle = window.adsbygoogle || []).push({});

http://www.ets.org/Media/Tests/GRE/pdf/Math.pdf [Broken]

59. A cyclic group of order 15 has an element x such that the set {x^3, x^5, x^9} has exactly two elements. The number of elements in the set {x^13n : n is a positive integer} is 3, 5, 8, 15 or infinite.

Obviously the answer can't be "infinite". Cyclic implies commutative, but don't know how to use this.

61. What is the greatest integer that divides (p^4) - 1 for every prime number p greater than 5? 12, 30, 48, 120 or 240

Does either Fermat's or Euler's theorem apply here somehow?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# GRE Practice Test Questions

Loading...

Similar Threads - Practice Test Questions | Date |
---|---|

Abstract algebra practice | Dec 24, 2011 |

Practice problem with invertible matrices | Dec 14, 2009 |

Practical Uses for Eigenvalues | May 8, 2009 |

Practical applications of number theory? | Sep 4, 2008 |

Practical pseudoprimality testing | Dec 1, 2005 |

**Physics Forums - The Fusion of Science and Community**