Question 350589: List all congruence classes module 7, with three elements in each.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Congruence Classes Modulo 7:
[0] = {..., -7, 0, 7, ...}
[1] = {..., -6, 1, 8, ...}
[2] = {..., -5, 2, 9, ...}
[3] = {..., -4, 3, 10, ...}
[4] = {..., -3, 4, 11, ...}
[5] = {..., -2, 5, 12, ...}
[6] = {..., -1, 6, 13, ...}
Note: Notice how [7] = {..., 0, 7, 14, ...} and that 0 and 7 are in [0]. It turns out that -7 is also in [7]. So basically this means that [0]=[7]. So we are done listing all the congruence classes (because any other class is equivalent to one of the classes shown above)
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