Modular multiplication multiplies numbers that wrap around after a chosen modulus. Reduce the product to its remainder: with modulus 5, 3 × 2 = 6 ≡ 1 mod 5. section 5.2.1
The modulus sets the wraparound point. Euclidean division supplies the remainder: 7 = 5 × 1 + 2, so 7 ≡ 2 mod 5. In the multiplicative group, 3 and 2 are inverses because their product is 1 modulo 5. section 5.2.1
Figure 5.5 The group of integers modulo the prime number 5 can be pictured as a clock that resets to 0 after the number 4. Thus 5 is represented as 0, 6 as 1, 7 as 2, 8 as 3, 9 as 4, 10 as 0, and so on.
Picture the integers modulo 5 as a clock: 5 resets to 0, 6 becomes 1, and 7 becomes 2. section 5.2.1
