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use generalized version of a property. Tag: Reverted |
Undid revision 1290821571 by 95.15.233.244 (talk)This was more general before. |
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* If {{math|''a'' + ''k'' ≡ ''b'' + ''k'' (mod ''m'')}}, where {{math|''k''}} is any integer, then {{math|''a'' ≡ ''b'' (mod ''m'')}}.
* If {{math|''k a'' ≡ ''k b'' (mod ''m'')}} and {{math|''k''}} is coprime with {{math|''m''}}, then {{math|''a'' ≡ ''b'' (mod ''m'')}}.
* If {{math|''k a'' ≡ ''k b'' (mod ''k m'')}} and {{math|''k'' ≠ 0}}, then {{math|''a'' ≡ ''b'' (mod ''m'')}}.
The last rule can be used to move modular arithmetic into division. If {{math|''b''}} divides {{math|''a''}}, then {{math|1=(''a''/''b'') mod ''m'' = (''a'' mod ''b m'') / ''b''}}.
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