(Solved): (1 point) This question concerns primality testing. Consider the composite number 305 . Recall Fer ...

(1 point) This question concerns primality testing. Consider the composite number 305 . Recall Fermat's Little Theorem: For any prime \( p \) and integer \( a, a^{p-1} \equiv 1 \bmod p \). It happens that the converse to FLT is often but not always true. That is, if \( n \) is composite and \( a \) is an integer, then more often than not \( a^{n-1} \not \equiv 1 \quad \) mod can use this as the basis of a simple primality test, called the Fermat Test. For \( a \in \mathbb{Z}_{305} \) we make the following definitions. 1) We call \( a \) a Fermat Liar for \( n=305 \) if \( a^{n-1} \equiv 1 \bmod n \), where \( a \notin(0,1, n-1) \). 2) We call \( a \) a Fermat Witness for \( n=305 \) if \( a^{n-1} \not 1 \bmod n \), where \( a \not \neq(0,1, n-1) \). Please answer the following. a) What is the first Fermat Liar in \( \mathbb{Z}_{305} \) ? b) What is the first Fermat Witness in \( \mathbb{Z}_{305} \) ? c) How many Fermat Liars are in \( \mathbb{Z}_{305} \) ? Remember not to count 0,1 , or \( n-1 \).