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Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
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?
What can you say about the common difference of an AP where every term is prime?