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Carom Maths provides this resource for teachers and students of A Level mathematics.

A repunit, which stands for repeated unit, is a number like 11, 111, or 1111 that contains only the digit 1 and extends to number bases other than base ten. This presentation challenges students to prove that any repunit having a composite (non-prime) number of digits must be composite. Theorems of Fermat and Euler are also applied to this thought provoking exercise.

The resource is designed to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon if necessary.

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