Thread: Norm Question....

Hi guys!

I've just looked at a past year's number theory questions and one is as follows:

Let R = Z[Sqrt(-6)] & K = Q[Sqrt(-6)]. Put a = 3+2Sqrt(-6) & b = 7-6Sqrt(-6). By choosing c close to b/a, or otherwise, find c in R such that:

Normk(b-ac) < Normk(a)

I have no ideas! :-s

Any help would be most appreciated! x

Originally Posted by AAM

Hi guys!

I've just looked at a past year's number theory questions and one is as follows:

Let R = Z[Sqrt(-6)] & K = Q[Sqrt(-6)]. Put a = 3+2Sqrt(-6) & b = 7-6Sqrt(-6). By choosing c close to b/a, or otherwise, find c in R such that:

Normk(b-ac) < Normk(a)

I have no ideas! :-s

Any help would be most appreciated! x

I assume . Form where by multiplying the numerator and denominator of by the conjugate. Next choose , intergers, so that are the closest integers to respectively. Set and see that .

Oh, fantastic! :-D Nice and simple! Just wasn't quite sure what the question was asking for. :-s But I completely get it now!

Thank you. :-)