Undergraduate Math Club Seminar

Series: Undergraduate Math Club Seminar Series

FERMAT'S LITTLE THEOREM AND EULER'S THEOREM IN THE GAUSSIAN INTEGERS

Milan Roberson, California Institute of Technology,

We will prove Fermat's Little Theorem using reduced residue systems and modular arithmetic (Ivory and Dirichlet) and briefly explore parity, primality, and Mersenne prime analogs in the Gaussian integers in order to motivate extending Fermat's Little Theorem to the Gaussian integers. We extend Euler's Theorem to the Gaussian integers and find a formula for computing Euler's phi function over the Gaussian integers

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For more information, please contact Mathematics Department by phone at 4335 or by email at [email protected].