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Prime AP
Age 16 to 18
Challenge Level 
First prove the common difference must be even and then that it must be divisible by 3. Think about possible remainders when the middle number is divided by 3. Consider two cases.
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Summats Clear
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.