RNT2.3.1. Euclidean Algorithm for Gaussian Integers

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Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identity in this case.
  1. MathDoctorBob
  2. mathematics
  3. ring
  4. theory
  5. abstract
  6. algebra
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Комментарии
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this is the best (only) treatment I can find of the Euclidean algorithm on Z[i] *thumbs-up*

mrcactu
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thanks heaps for your videos dr bob.  im doing a major in pure mathematics and you cover so many of the relevant topics in your videos.  

signorcroach
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Much more helpful than my prof ! Thank you!

ameyzhang
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Fields are always Euclidean domains, but not very exciting as such - every nonzero element u is a unit, so d(1) = d(u) and the Euclidean algorithm is always solved in Step 1.

Lattices in C are a big deal in number theory though.

MathDoctorBob
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generalize Euclid's algorithm to complex numbers?

wdlang