If we find our self's in need to calculate a Legendre's symbol such that p\a ,what should we do?If we find our self's in need to calculate a Legendre's symbol such that p\a ,what should we do ?
Hi Minas. The value of the Legendre symbol (a/p), with p|a, depends on your preferred definition. In the lectures, I did not define the symbol in that case; however, in most sources, it is defined as (a/p)=0. Should this case appear in the exam, I will accept both.
The reason why I chose not to define it in this case, is because I was considering talking about characters and the Legendre/Jacobi symbol is a character of Z_n^*.
The reason why I chose not to define it in this case, is because I was considering talking about characters and the Legendre/Jacobi symbol is a character of Z_n^*.