Some problems in Number Theory

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Number theory - the study of the natural numbers - does not typically feature in school curricula, but it is a rich source of interesting problems which can lead to surprising results. The problems in this feature will offer you the opportunity to notice patterns, conjecture, generalise and prove results.

Many results can be explained by applying GCSE algebraic techniques, and many can also be explained using diagrams or pictorial representations.

Number theory is studied in more detail at university, and it is often seen as one of the "purest" forms of mathematics.  Gauss said "Mathematics is the queen of the sciences - and number theory is the queen of mathematics".

You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these problems.

We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.