MathDB
B 4

Source:

May 25, 2007
modular arithmeticPrimitive Roots

Problem Statement

Let gg be a Fibonacci primitive root (modp)\pmod{p}. i.e. gg is a primitive root (modp)\pmod{p} satisfying g2≡g+1  (modp)g^2 \equiv g+1\; \pmod{p}. Prove that [*] g−1g-1 is also a primitive root (modp)\pmod{p}. [*] if p=4k+3p=4k+3 then (g−1)2k+3≡g−2(modp)(g-1)^{2k+3} \equiv g-2 \pmod{p}, and deduce that g−2g-2 is also a primitive root (modp)\pmod{p}.
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