Some Facts from Number Theory

m ƒ qn‚ r , and 0 r < jnj. Not surprisingly, q is the quotient and r is the remainder when m is divided by n.1 We say that n divides m, or n is a divisor of m, when the remainder is zero. The notation n jm is used to signify that n divides m. An integer p is a prime number if 1 < jpj and the only divisors of p are 1 and p. We write a b „mod n… if b a is divisible by n.2 This notion, called congruence, is an equivalence relation. All the usual laws of arithmetic hold for congruence; for example, we have the distributivity of multiplication over addition and the associativity of multiplication.