Reasoning, convincing and proving

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Modulus 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.
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Transitivity

Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics.
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More sums of squares

Tom writes about expressing numbers as the sums of three squares.
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Sums of squares and sums of cubes

An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.
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Modulus arithmetic and a solution to differences

Peter Zimmerman, a Year 13 student at Mill Hill County High School in Barnet, London wrote this account of modulus arithmetic.
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Magic squares II

An article which gives an account of some properties of magic squares.
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Why stop at three by one

Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.
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Picturing Pythagorean triples

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
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Where do we get our feet wet?

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
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Telescoping functions

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.