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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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Prime AP

What can you say about the common difference of an AP where every term is prime?

Summats Clear

Age 16 to 18 Challenge Level:

Find the sum, $f(n)$, of the first $n$ terms of the sequence: \begin{equation*} 0, 1, 1, 2, 2, 3, 3, \dots , p, p, p +1, p + 1, \dots \end{equation*}

Go on to prove that $f(a + b) - f(a - b) = ab$, where $a$ and $b$ are positive integers and $a > b$.