Recent content by 2e4L

  1. 2

    prove that the group U(n^2 -1) is not cyclic

    It may be because it's still fairly early in the course. I learned the Chinese Remainder Theorem in a number theory class, but have yet to encounter it in my current one. We are going to study rings after the upcoming exam. The previous problem was in a different chapter of the text I believe...
  2. 2

    prove that the group U(n^2 -1) is not cyclic

    I have learned that property of Euler's totient function, but not the one about U(ab) = U(a) x U(b). I've come across it online, but have yet to use it in class. Is there another method?
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    Is Assuming the Consequent a Valid Proof Method?

    Euclid's lemma: If p is a prime and divides ab (p|ab), then p|a or p|b
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    prove that the group U(n^2 -1) is not cyclic

    Sorry if I formatted this thread incorrectly as its my first post ^^ Homework Statement For every integer n greater than 2, prove that the group U(n^2 - 1) is not cyclic. Homework Equations The Attempt at a Solution I've done a problem proving that U(2^n) is not cyclic when...