Number theory

There are 34 NRICH Mathematical resources connected to Number theory
Always Perfect
problem
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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
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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?
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?
Where can we visit?
problem
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Where can we visit?

Age
11 to 14
Challenge level
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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Number rules - OK
problem
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Number rules - OK

Age
14 to 16
Challenge level
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Can you produce convincing arguments that a selection of statements about numbers are true?

How much can we spend?
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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?
There's a limit
problem
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There's a limit

Age
14 to 18
Challenge level
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Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
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?

Differences
problem
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Differences

Age
11 to 14
Challenge level
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Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?