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# Prime AP

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Age 16 to 18

Challenge Level

Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6.

Find some examples of three primes which include the number 3 and form an AP, and show that in every such case the common difference is not divisible by 6.

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.