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smc

number theory senior

Problem

Consider the statement, "If is not prime, then is prime." Which of the following values of is a counterexample to this statement?
(A)
(B)
(C)
(D)
(E)
Solution
Since a counterexample must be a value of which is not prime, must be composite, so we eliminate and . Now we subtract from the remaining answer choices, and we see that the only time is not prime is when .
Final answer
E