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Fibonacci Factors

Age 16 to 18
Challenge Level Yellow star
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In the Fibonacci sequence each term is the sum of the two terms before it:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

Where do the even numbers come in the sequence?

Is there a pattern? Why?

Which Fibonacci numbers are divisible by 3?

Prove general results for the occurrence of even Fibonacci numbers in the sequence and for the occurrence of multiples of 3.

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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.

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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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