- #1

- 1,270

- 0

## Main Question or Discussion Point

"Let p be an odd prime, then we proved that the Legendre symbol

Note that this can be easily computed

For example, if p=59, then p≡3 (mod 8) and [tex](-1)^{(p^2-1)/8}[/tex] = [tex](-1)^{(3^2-1)/8}[/tex]" (quote from my textbook)

====================================

Now I don't exactly see WHY p can be reduced modulo 8 without changing the answer.

Why can we be so sure that [tex](59^2-1)/8[/tex] and [tex](3^2-1)/8[/tex] will have the same parity? How can we prove this?

Thanks for explaining!

Note that this can be easily computed

**if p is reduced modulo 8**.For example, if p=59, then p≡3 (mod 8) and [tex](-1)^{(p^2-1)/8}[/tex] = [tex](-1)^{(3^2-1)/8}[/tex]" (quote from my textbook)

====================================

Now I don't exactly see WHY p can be reduced modulo 8 without changing the answer.

Why can we be so sure that [tex](59^2-1)/8[/tex] and [tex](3^2-1)/8[/tex] will have the same parity? How can we prove this?

Thanks for explaining!