- #1
thomas430
- 17
- 0
Hi all,
so I was looking at Legendre symbols, and I saw that [tex]\left(\frac{2}{p}\right)=(-1)^{\frac{p^2-1}{8}}[/tex].
How does one show that [tex]\frac{p^2-1}{8}[/tex] is always an integer? That is, how can we show that [tex]8 | p^2-1[/tex]?
Can a similar method be applied to show that [tex]24 | p^3-p[/tex]?
Thanks :-)
Thomas.
so I was looking at Legendre symbols, and I saw that [tex]\left(\frac{2}{p}\right)=(-1)^{\frac{p^2-1}{8}}[/tex].
How does one show that [tex]\frac{p^2-1}{8}[/tex] is always an integer? That is, how can we show that [tex]8 | p^2-1[/tex]?
Can a similar method be applied to show that [tex]24 | p^3-p[/tex]?
Thanks :-)
Thomas.