I am reading the book Introduction to Modern Cryptography second edition by Katz et al.
The Jacobi Symbol is defined on page 536 and I have included a picture below.
I was able to understand most of this video on solving Jacobi Symbol equations. Provided this is not off topic to what the book requires, I have some questions about some of the different examples from the video.
1:14 Why did he flip the fraction here, take away one, and then divide?
2:28 If the top (called 'a') is a number that can be expressed as a square, then it equals 1? Why did he not flip the fraction like he earlier at 1:14?
I think the answer for the above question 1 and 2 is you only flip it when there is not a number at the top which can be the product of a square?
4:51 Why is this answer -1, I thought 2 (mod 3) = 2?
I did think when using Jacobi Symbols the top number had to be larger than the bottom number, but it does not always seem to be the case here?
The above questions I have seem to happen throughout the video, so I will avoid asking the same question numerous times.
