 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2003/calculus-probability-linear-algebra-discrete-mathematics-logic-and-proof-and-models-of-computation/6/a/iii/solution

x

y

have the same remainder and

x

z

have the same remainder, then

y

z

have the same remainder. In the notation of modular arithmetic,

x \equiv y (mod 8), x \equiv z (mod 8) ⟹ y \equiv z (mod 8) .

Hence

MOD 8 is Euclidean .

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