Number theory

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An introduction to number theory

An introduction to some beautiful results in Number Theory.
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Favourite

Always perfect

Age

14 to 18

Challenge level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
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Impossibilities

Age

11 to 14

Challenge level

Just because a problem is impossible doesn't mean it's difficult...
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Overlaps

Age

11 to 14

Challenge level

Can you find ways to put numbers in the overlaps so the rings have equal totals?
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Binomial coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
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Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?
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A little light thinking

Age

14 to 16

Challenge level

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
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Favourite

How much can we spend?

Age

11 to 14

Challenge level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
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Data chunks

Age

14 to 16

Challenge level

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and blue chunks, explore what sizes near to 31 can, or cannot, be exactly filled.
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The public key

Age

16 to 18

Challenge level

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.