Patrick Dugan

Patrick Dugan

he/him

M.S.E./B.S.E. in CS and B.A. in Math at Penn. Combinatorics, learning theory, ML systems.

Factoring Polynomials in Arbitrary Fields

less than 1 minute read

Published:

This is part 2 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.

This part shows how polynomials factor over an arbitrary field, covers minimal polynomials and divisibility, and proves the key fact for part 3: a nonzero polynomial has no more roots than its degree.

Part 3 ends with an interactive version you can play with: watch (Z/pZ)× turn out cyclic.

Read the write-up (PDF)

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Published:

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