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Be Reasonable

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

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Janusz Asked

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?

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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.

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?