Diophantine N-tuples

Can you explain why a sequence of operations always gives you perfect squares?

DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.

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Age 14 to 16 Challenge Level:

At what distance down the corridor will the ray of light pass through the centre line again?

At what distance down the corridor will the ray of light pass through the centre line again going in the same direction as it was initially?

Creating and manipulating expressions and formulae. Sine, cosine, tangent. Polynomial functions and their roots. Mathematical reasoning & proof. Pythagoras' theorem. Regular polygons and circles. 2D shapes and their properties. Reflections. Inequalities. Generalising.

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Diophantine N-tuples

DOTS Division

Sixational

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Age 14 to 16 Challenge Level: