group-theory
The group U(n)
taught
Taught in
-
Units modulo n and the group U(n)
Group Theory
Requires
- integers-mod-n-group required
-
eulers-totient-function
helpful
|U(n)| equals phi(n), but that fact is established only after U(n) itself is built and studied (ch.03 secs 3-5, deliberately concrete-before-abstract) -- defining U(n) and verifying it's a group needs only modular multiplicative inverses, not phi(n)'s value.
Required by
- Euler's theorem, proved via Lagrange required
- Order of elements in Z_n and U(n) required
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