# Resources tagged with: Divisibility

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### There are 31 results

Broad Topics > Properties of Numbers > Divisibility

### 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.

### Sixational

##### Age 14 to 18Challenge Level

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

### Prime AP

##### Age 16 to 18Challenge Level

What can you say about the common difference of an AP where every term is prime?

### Modulus Arithmetic and a Solution to Dirisibly Yours

##### Age 16 to 18

Peter Zimmerman from Mill Hill County High School in Barnet, London gives a neat proof that: 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

### Dirisibly Yours

##### Age 16 to 18Challenge Level

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

### Elevens

##### Age 16 to 18Challenge Level

Add powers of 3 and powers of 7 and get multiples of 11.

### Obviously?

##### Age 14 to 18Challenge Level

Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.

### The Chinese Remainder Theorem

##### Age 14 to 18

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."

### Latin Numbers

##### Age 14 to 16Challenge Level

Can you create a Latin Square from multiples of a six digit number?

### Multiple Surprises

##### Age 11 to 16Challenge Level

Sequences of multiples keep cropping up...

### Public Key Cryptography

##### Age 16 to 18

An introduction to coding and decoding messages and the maths behind how to secretly share information.

### Knapsack

##### Age 14 to 16Challenge Level

You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.

### The Knapsack Problem and Public Key Cryptography

##### Age 16 to 18

An example of a simple Public Key code, called the Knapsack Code is described in this article, alongside some information on its origins. A knowledge of modular arithmetic is useful.

### Transposition Fix

##### Age 14 to 16Challenge Level

Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine. . . .

### Check Codes

##### Age 14 to 16Challenge Level

Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check. . . .

### Take Three from Five

##### Age 11 to 16Challenge Level

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

### Code to Zero

##### Age 16 to 18Challenge Level

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

### Mod 3

##### Age 14 to 16Challenge Level

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

### Multiplication Magic

##### Age 14 to 16Challenge Level

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

### Odd Stones

##### Age 14 to 16Challenge Level

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

### Divisibility Tests

##### Age 11 to 16

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

### Why 24?

##### Age 14 to 16Challenge Level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

### Fac-finding

##### Age 14 to 16Challenge Level

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

### 396

##### Age 14 to 16Challenge Level

The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.

### Expenses

##### Age 14 to 16Challenge Level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

### Big Powers

##### Age 11 to 16Challenge Level

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

### Squaresearch

##### Age 14 to 16Challenge Level

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

### N000ughty Thoughts

##### Age 14 to 16Challenge Level

How many noughts are at the end of these giant numbers?

### Ben's Game

##### Age 11 to 16Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

### There's Always One Isn't There

##### Age 14 to 16Challenge Level

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

### LCM Sudoku

##### Age 14 to 16Challenge Level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.