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Fibonacci Factors

Age 16 to 18
Challenge Level Yellow star
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The Fibonnaci sequence occurs so frequently because it is the solution of the simplest of all difference relations. It is instructive to view it in this way and perhaps to introduce the idea of difference equations with this familiar example.

Proving these results calls for considering whether or not other terms in the sequences, apart from those in the recognized patterns, can also be multiples of 2 or 3 respectively in the two cases. Are the conditions necessary as well as sufficient?


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Code to Zero

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.

Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Parabella

This is a beautiful result involving a parabola and parallels.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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