Stage: 4 Challenge Level: 
Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6. Find some examples of three primes which include the number 3 and form an AP, and show that in every such cases the common difference is not divisible by 6.
Mathematical reasoning & proof. Modulus arithmetic. Generalising. Divisibility. Manipulating algebraic expressions/formulae. Number theory. Patterned numbers. Inequality/inequalities. Visualising. Arithmetic sequence.
Published February 2002.
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