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There are 11 NRICH Mathematical resources connected to Number theory, you may find related items under Properties of numbers.
Broad Topics > Properties of numbers > Number theoryCan you find ways to put numbers in the overlaps so the rings have equal totals?
Just because a problem is impossible doesn't mean it's difficult...
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?
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
What is the remainder when 2^{164}is divided by 7?
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.
All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?