**24**

Congruence modulo a prime

In this final chapter we consider a number of results concerning expressions which are automatically divisible by some given prime number. The results given here have their origins in the seventeenth century but it is convenient to formulate and prove them using the idea of congruence.

Although the results may appear only to be of theoretical interest these ideas do in fact provide an important ingredient in the techniques of public-key cryptography using prime numbers referred to in the previous chapter. Furthermore the ideas introduced in this chapter led to the development of group theory, the study of symmetry, which is now an enormously rich subject with many applications both within mathematics and in many ...

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