Show that a^2 -1 = 0 mod p has only 2 solutions

I have an exercise for a course in Cryptography. One of the questions asks us to show that the equation a^2 -1 = 0 mod p has only 2 solutions.

we are told to consider the group Z sub p whose elements are {1,2,.....,p-1}.

I am having a hard time even finding a starting point for this problem. Can anyone give me some advice?

Re: Show that a^2 -1 = 0 mod p has only 2 solutions

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**restin84** I have an exercise for a course in Cryptography. One of the questions asks us to show that the equation a^2 -1 = 0 mod p has only 2 solutions.

we are told to consider the group Z sub p whose elements are {1,2,.....,p-1}.

I am having a hard time even finding a starting point for this problem. Can anyone give me some advice?

Re: Show that a^2 -1 = 0 mod p has only 2 solutions