| The associated ring of integers is [θ] with θ = 2 . | This is a principal ring and for X, Y ∈ [θ], | | | | | We verify that gcd(X, Y) divides both X and Y. | | | The coefficients U, V of the extended gcd are | | | | The Bézout identity in [θ] is UX + VY = gcd(X,Y), that is, | | | | The fundamental unit here is ε = -1. | Then any element of the form (100θ+100) is also a gcd of X, Y. |
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