# Resources tagged with: Number theory

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### There are 25 results

Broad Topics > Properties of Numbers > Number theory ### There's a Limit

##### Age 14 to 18Challenge Level

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? ### Diophantine N-tuples

##### Age 14 to 16Challenge Level

Can you explain why a sequence of operations always gives you perfect squares? ### How Much Can We Spend?

##### Age 11 to 14Challenge 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? ### Marbles

##### Age 11 to 14Challenge Level

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? ### Always Perfect

##### Age 14 to 18Challenge Level

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

##### Age 11 to 14Challenge Level

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? ### A One in Seven Chance

##### Age 11 to 14Challenge Level

What is the remainder when 2^{164}is divided by 7? ### Ordered Sums

##### Age 14 to 16Challenge Level

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . . ### A Little Light Thinking

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge 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. . . . ### Impossibilities

##### Age 11 to 14Challenge Level

Just because a problem is impossible doesn't mean it's difficult... ### Number Rules - OK

##### Age 14 to 16Challenge Level

Can you produce convincing arguments that a selection of statements about numbers are true? ### Really Mr. Bond

##### Age 14 to 16Challenge Level

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise? ### Euler's Squares

##### Age 14 to 16Challenge Level

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square... ### Where Can We Visit?

##### Age 11 to 14Challenge Level

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? ### Never Prime

##### Age 14 to 16Challenge Level

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime. ### Got it Article

##### Age 7 to 14

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy. ### Differences

##### Age 11 to 14Challenge Level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number? ### Filling the Gaps

##### Age 14 to 16Challenge Level

Which numbers can we write as a sum of square numbers? ### Strange Numbers

##### Age 11 to 14Challenge Level

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. . . . ### Overlaps

##### Age 11 to 14Challenge Level

Can you find ways to put numbers in the overlaps so the rings have equal totals? ### The Codabar Check

##### Age 11 to 14

This article explains how credit card numbers are defined and the check digit serves to verify their accuracy. ### Novemberish

##### Age 14 to 16Challenge Level

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. ### An Introduction to Modular Arithmetic

##### Age 14 to 18

An introduction to the notation and uses of modular arithmetic ### Binomial Coefficients

##### Age 14 to 18

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