"Let p be an odd prime, then we proved that the Legendre symbol(adsbygoogle = window.adsbygoogle || []).push({});

Note that this can be easily computedif 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)

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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!

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# Legendre Symbol (2/p)

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