Assume the values of the variables are restricted so that the expressions are defined.
Exercise
a. Prove that n! + 2 is divisible by 2, for all integers n ≥ 2.
b. Prove that n! + k is divisible by k, for all integers n ≥ 2 and k = 2, 3, ..., n.
c. Given any integer m ≥ 2, is it possible to find a sequence of m – 1 consecutive positive integers none of which is prime? Explain your answer.
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