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Broad Topics > Algebraic expressions, equations and formulae > Identities

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Powerful Factors

Age 16 to 18 Challenge Level:

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.

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Binomial

Age 16 to 18 Challenge Level:

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

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Proofs with Pictures

Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities.

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Particularly General

Age 16 to 18 Challenge Level:

By proving these particular identities, prove the existence of general cases.