Stage: 5 Challenge Level: 
Factorise $5^{36}-1$ into as many factors as you can, until you can calculate the values and see which ones are even and which are multiples of $3$.
Modulus arithmetic. Factors and multiples. Quadratic equations. Manipulating algebraic expressions/formulae. Index notation/Indices. Factorisation (algebraic). Identities. Long problems. Pythagoras' theorem. Mathematical reasoning & proof.
Published June 1998.
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