Why 134mod−26 is equal 22? I found an explanation, which says: 134=(−26⋅−6)−22 However, 134=(−26⋅−5)+4, so why 134mod−26 is not equal 4 if 134=(26⋅5)+4⇒134mod26=4 All i could find, is about a situation, if i take a modulo of negative number (−134mod26), but that is not what i want.

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Why 134mod−26 is equal 22?   I found an explanation, which says: 134=(−26⋅−6)−22   However, 134=(−26⋅−5)+4, so why 134mod−26 is not equal 4   if 134=(26⋅5)+4⇒134mod26=4   All i could find, is about a situation, if i take a modulo of negative number (−134mod26), but that is not what i want.

Eliza Norris · Accepted Answer

The first sentence in the post is wrong. −136 in not congruent to 22 modulo −26. It is congruent to −22.   In the second sentence you had an error (now fixed). You mean −26*−5.   4 and −22 are the same answer modulo −26 since they differ by a multiple of −26.   Arithmetic modulo m is essentially the same as arithmetic modulo −m.   Sometimes you want to require an answer that lies between 0 and the positive value |m|−1, sometimes any equivalent answer will do.   If you are working with or writing a computer program to do modular arithmetic the program will make a choice - usually the representative between 0 and |m|−1.

Why 134 mod -26 is equal 22? I found an explanation, which says: 134 = (-26 * -6

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