Stage: 4 Challenge Level: 
Why do this problem?
It gives practice in factorisation and an opportunity for learners to make and prove conjectures.
Possible approach
This problem makes a good lesson starter.
Key questions
What are the factors of $n^5 - n$?
Factorisation (algebraic). Generalising. Factors and multiples. Common factors. Manipulating algebraic expressions/formulae. Polynomials. Inequality/inequalities. Stage 5 - Reviewed 2012. Mathematical reasoning & proof. Number theory.
Published October 2001.
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