12).

Similarly, if one waits 8 hours and then 8 more hours (thus 16 hours in total), the clock will show the same time change as if one waited 4 hours. This is reflected by the identity 2 × 8 ≡ 4 (mod 12). After a wait of exactly 12 hours, the hour hand will be right where it started, so 12 acts as 0; one writes 12 ≡ 0 (mod 12).

Congruence

Given an integer , called a modulus, two integers and are said to be congruent modulo , if their difference is an

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