question concerns primality testing. Recall Fermat's Little Theorem: For any prime p and integer a, a-1 = 1 mod 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"- #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a E Z, we make the following definitions. 1) We call a a Fermat Liar for n if a"-1 =1 mod n, where a (0, 1, n – 1). 2) We call a a Fermat Witness for n if a"-I #1 mod n, where a ¢ (0, 1, n- 1). If a number is composite, then 2 is very often a Fermat Witness. What is the smallest composite integer n greater than 9796 for which 2 is not a Fermat Witness?

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.