 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2010/c/c2/v/solution

By (ii), failure of divisibility is equivalent to

q - 1 ∣ 30

. The positive divisors of

30

are

1, 2, 3, 5, 6, 10, 15, 30

; adding one gives

2, 3, 4, 6, 7, 11, 16, 31

. Retaining only primes yields

q \in {2, 3, 7, 11, 31} .

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