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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}.

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Novemberish

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

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Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Number Rules - OK

Age 14 to 16 Challenge Level:

Try some numbers first - are you convinced?

For part two-

Now try to write the product or quotient of two square numbers in a general form - can you rewrite this expression so that it is a (a number) squared?

For part three -

What are all the possibilities for the units digit when you square any whole number?