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Algebra question

Hey, I'm having difficulty in answering the last part of question 2, the one that reads.."By considering a = 3 − 2 2, prove that the group of invertible elements of Z[ 2] is infinite."

It'd be very much appreciated if someone could provide me With the proof of this as it would help me to understand how to apply it to similar questions! Many thanks for any response ☺️ImageUploadedByStudent Room1457892838.691840.jpg


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maths10101
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@Zacken
Not sure if the tagging is working??


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@Zacken
Original post by maths10101
Hey, I'm having difficulty in answering the last part of question 2, the one that reads.."By considering a = 3 − 2 2, prove that the group of invertible elements of Z[ 2] is infinite."

It'd be very much appreciated if someone could provide me With the proof of this as it would help me to understand how to apply it to similar questions! Many thanks for any response ☺️ImageUploadedByStudent Room1457892838.691840.jpg


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I moved this to the right forum for you :smile:
(edited 8 years ago)
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Zacken
22
Original post by maths10101
Hey, I'm having difficulty in answering the last part of question 2, the one that reads.."By considering a = 3 − 2 2, prove that the group of invertible elements of Z[ 2] is infinite."It'd be very much appreciated if someone could provide me With the proof of this as it would help me to understand how to apply it to similar questions! Many thanks for any response ☺️ImageUploadedByStudent Room1457892838.691840.jpgPosted from TSR Mobile
Moved to maths, please post your question in the maths forum in the future.You essentially want to prove that there are an infinite number of solutions to a2−2b2=±1a^2 - 2b^2 = \pm 1, them asking you to consider 3−223 - 2\sqrt{2} was so you could guess that if (a,b)(a, b) is a positive solution to the above equation (b<ab < a) then (a+2b,a+b)(a+2b, a+b) is also another solution - can you prove that this is true? It's just a bunch of plugging in.
Original post by Kvothe the arcane
Thank you.
Original post by Zacken
Thank you.


You're welcome :h:. Thanks for your help.
Reply 6
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Zacken
22
It's basic first year algebra.

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