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 | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# GRE Practice Test Questions

**Physics Forums | Science Articles, Homework Help, Discussion**