 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2012/c/c1/d/solution

30

30

are

1, 7, 11, 13, 17, 19, 23, 29.

There are eight, so

φ (30) = 8

. Their sum can be grouped into four pairs summing to

30

1 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 120 = \frac{1}{2} \cdot 30 \cdot 8.

This agrees with the formula.

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