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5. Determine that True or False and explain why. (1) There exists always the least number \( r \in Z^{+} \)such that \( a^{r} \equiv 1(\bmod m) \). (2) If \( g \) is a primitive root of \( m(\geq 3) \) then \( g^{1}+g^{2}+\cdots+g^{\varphi(m)} \equiv 0(\bmod m) \). (3) There is primitive root of 77 .

Given two whole numbers An and M, find the particular multiplicative reverse of An under modulo M. The measured multiplicative reverse is a whole numb