PMATH340 LN8

Note that every element in a zn has an additive

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Unformatted text preview: c ≡ bd(mod n). Remark 5. The arithmetic, “+, −, ·” with congruences is the same as the arithmetic “+, −, ·” in integers. But here we are only interested in remainders. Example 6. We have 19 ≡ 11(mod 4) 6 ≡ 2(mod 4) 13 ≡ 19 − 6 ≡ 11 − 2 ≡ 11 − 2 = 9(mod 4) 114 ≡ 19 · 6 ≡ 11 · 2 = 22 ≡ 2(mod 4). Definition 9. The set Zn := {0, 1, 2, . . . , n − 1} equipped with addition and multiplication modulo n is called the ring of integers modulo n. Note that every element in a ∈ Zn has an additive inverse (there is an element b...
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