It boasts of the most famous and popular mathematical puzzle of all time - Fermat's Last Theorem, only recently proved by Andrew Wiles. Things have changed dramatically in recent years, especially with the invention of public-key cryptography, and number theory has suddenly accepted a great deal of responsibility for the world's efficient functioning. The purpose of this half-paper is twofold, and the targeted audience of students is very broad. The first aim is to cover the basics of elementary number theory that every mathematician should, in theory, know something about - such as divisibility, prime numbers and their distribution, congruences, up to and including elements of analytic number theory. The second aim is to outline some ideas behind present-day cryptosystems.
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