11. Find a greatest common divisor d, of a and b in the Euclidean Domain, expressed as d = ua + vb where a = 4 + 7i b = 8 - i in Z[i]
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Since 4 is a factor of any even number, the GCD will be 4 if n is even, and 1 if n is odd. Now, we need to express the GCD as a linear combination of 4 and n, i.e., d = u * 4 + v * n, where u and v are integers. Case 1: n is even (n = 2k for some integer k) In Show more…
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