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→Congruence: unneeded pedantry |
→Congruence: no pedantry, operations defined are not trivial like ordinary addition of integers calculator Tag: Reverted |
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Given an [[integer]] {{math|''m'' ≥ 1}}, called a '''modulus''', two integers {{mvar|a}} and {{mvar|b}} are said to be '''congruent''' modulo {{mvar|m}}, if {{mvar|m}} is a [[divisor]] of their difference; that is, if there is an integer {{math|''k''}} such that
: {{math|1=''a'' − ''b'' = ''k m''}}.
Congruence modulo {{mvar|m}} is a [[congruence relation]], meaning that it is an [[equivalence relation]] that is compatible with defining
operations such as [[addition]], [[subtraction]], and [[multiplication]]. Congruence modulo {{mvar|m}} is denoted : {{math|''a'' ≡ ''b'' (mod ''m'')}}.
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