Elementary group theory and number theory questions involving prime numbers, permutation groups and dihedral groups. Introduction to number theory questions
Elementary group theory and number theory questions involving prime numbers, permutation groups and dihedral groups. Introduction to number theory questions.
Question 6 c) can be unanswered
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Alessandro Iraci
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very impressive, few questions if you dont mind, at the bottom of the first page and top of the second page the working is cut off, could you clarify what these 2 lines say? Also for question 4, when you say use a computer, what calculations have you done to find m?
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The two lines are repeated in the next page, so actually there is nothing cut off, don't worry! About question 4, I don't know exactly what the computer does, but I believe it relies on Bezout's theorem. You can find a construction with an explicit example here, in Example 4.2.5 https://math.libretexts.org/Courses/Mount_Royal_University/MATH_2150%3A_Higher_Arithmetic/4%3A_Greatest_Common_Divisor_least_common_multiple_and_Euclidean_Algorithm/4.2%3A_Euclidean_algorithm_and__Bezout%27s_algorithm
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also in question 1 when you write 'now suppose that...' what follows this as I read it as 'WLOG' which im sure its not lol
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Oh sorry I thought that was common knowledge: WLOG means "without loss of generality", meaning it doesn't matter if m > n or n > m, so we just pick one.
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Let me know if I should clarify it further, especially about Bezout's theorem!
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Okay that clears most of it up but just regarding question 4 it says the proof should give you a method which allows you to calculate a point in the sequence and to illustrate this method, I’m just wondering is there a way to illustrate this without a computer? Thanks so much for your help
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I will check tomorrow if the computation with Bezout's theorem can be done by hand.
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I uploaded the computation. It's a bit tedious but it's exactly as in the example.
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Thank you very much Alessandro
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You're welcome!
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This is a set of 5 multiple-part question, and can easily take over 2-3 hours to answer. The offered bounty is low.
thanks for advice, I have increased the bounty by 45%
What are we supposed to do about the Sage part?
this part can be unanswered, I will update description
Increased bounty again.
What is the alternating group A_n mentioned at the beginning? I suppose is the subgroup of S_n of even permutations, but it's not mentioned and I wanted to double-check.
sorry for slight delayed response I had to confirm with my tutor, yes that is what it means