Number theory

There are 34 NRICH Mathematical resources connected to Number theory
Always Perfect
problem
Favourite

Always Perfect

Age
14 to 18
Challenge level
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Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Impossibilities
problem
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Impossibilities

Age
11 to 14
Challenge level
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Just because a problem is impossible doesn't mean it's difficult...
Overlaps
problem
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Overlaps

Age
11 to 14
Challenge level
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Can you find ways to put numbers in the overlaps so the rings have equal totals?
Placeholder: several colourful numbers
article

Binomial Coefficients

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

Age
14 to 16
Challenge level
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Which numbers can we write as a sum of square numbers?
A little light thinking
problem
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A little light thinking

Age
14 to 16
Challenge level
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Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

How much can we spend?
problem
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How much can we spend?

Age
11 to 14
Challenge level
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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?
Data Chunks
problem

Data Chunks

Age
14 to 16
Challenge level
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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.
The Public Key
problem

The Public Key

Age
16 to 18
Challenge level
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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.