Stage: 5 Challenge Level: 
Prove that $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{5}$ cannot be terms
of ANY arithmetic progression.
[See the Proof Sorter . This is not the same proof but it may give you some ideas.}
[See the Proof Sorter . This is not the same proof but it may give you some ideas.}
Surds. Pythagoras' theorem. Mathematical reasoning & proof. Modulus arithmetic. Proof by contradiction. Long problems. Rational and irrational numbers. Quadratic equations. Arithmetic sequence. Geometric sequence.
Published April 1999.
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