Chapter 6 Congruences with a prime modulus

We met an example in the last chapter, where a single congruence \(\text{mod }(n)\) is equivalent to a set of simultaneous congruences modulo the prime powers \(p^e\) appearing in the factorisation of \(n\). In this chapter we will study congruences \(\text{mod }(p)\), where \(p\) is prime. In this case we shall see that in addition to modular addition, subtraction and multiplication, cancellation works more smoothly.