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From fermat's little theorem we have for

**a**prime to a prime**p**: [tex]a^{p-1}\equiv 1[/tex](mod p). Assuming p-1 to be even we must have either [tex]a^{\frac{p-1}{2}}\equiv 1[/tex] (mod p) or [tex]a^{\frac{p+1}{2}}\equiv -1[/tex] (mod p). Are there any special cases in which it is easy to determine which of the previous two conditions holds without a lot of compution?
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