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Divisibility tests
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
Divisibility
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articleModulus arithmetic and a solution to dirisibly yours
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. -
articleThe knapsack problem and public key cryptography
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. -
articleThe Chinese remainder theorem
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."
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articleDigital roots
In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers. -
articlePublic key cryptography
An introduction to coding and decoding messages and the maths behind how to secretly share information. -
problemCode to zero
Age16 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. -
problemN000ughty thoughts
Age14 to 16Challenge level
How many noughts are at the end of these giant numbers? -
problemMod 3
Age14 to 16Challenge level
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3. -
problemNovemberish
Age14 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.