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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.

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# Divisibility of powers of primes

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