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Euclidean Rings

Prove that in a Euclidean ring ( a , b ) can be found as follows

b = q0 a + r1 where d ( r1) < d (a )

a = q1 r1 + r2 where d ( r2) < d (r1 )

r1 = q1 r1 + r2 where d ( r3) < d ( r2 )

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rn-1 = qn rn

and rn = ( a , b )

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Solution Summary

Euclidean Rings are investigated.

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