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Why do this problem?
A non standard problem on prime numbers and AP's that requires some careful mathematical reasoning
Possible approach
Let the class work at first individually and then is small groups. Discuss their findings. If they have not met modulus arithmetic, or the usual notation, then introduce this notation as a standardised way of recording the reasoning in this solution.
Key questions
How can we be sure we have considered all possible cases?
Prime AP
Age 16 to 18
Challenge Level 
Why do this problem?
A non standard problem on prime numbers and AP's that requires some careful mathematical reasoning
Possible approach
Let the class work at first individually and then is small groups. Discuss their findings. If they have not met modulus arithmetic, or the usual notation, then introduce this notation as a standardised way of recording the reasoning in this solution.
Key questions
How can we be sure we have considered all possible 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.