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Problem involving irreducible element -Ring theory
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[QUOTE="chwala, post: 6866971, member: 287397"] ... I am trying to follow this with a practical example...i still have doubts on the highlighted, let us consider; the gcd ##(7,4)## with ##n=-2## for example, then we shall have (using Euclid algorithm), ##7=1⋅4+3## ... ##\dfrac{7}{4}= \dfrac{7(l-m\sqrt{-2})}{l^2+2m^2}=\dfrac{7l}{l^2+2m^2}-\dfrac{m\sqrt{-2}}{l^2+2m^2}## that is by following the attached literature... then ##\dfrac{t}{M}=\dfrac{7l}{l^2+2m^2}## and ##\dfrac{s\sqrt{n}}{M}=\dfrac{m\sqrt{-2}}{l^2+2m^2}## ...let ##X, Y## be the closest integers to the two ratios on the right...not quite understanding this statement...do they mean ##X## an integer value i.e close to ##\dfrac{7l}{l^2+2m^2}## and ##Y## an integer value close to ##\dfrac{m\sqrt{-2}}{l^2+2m^2}##? [/QUOTE]
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Problem involving irreducible element -Ring theory
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