Let m 3 and let a1 am be a reduced residue system modulo

Let m 3, and let {a₁, . . . , a_(m)} be a reduced residue system modulo m (any RRS, not one in particular!). Show that the sum a₁ + · · · + a_(m) is divisible by m.

Solution

Reduced residue system modulo m means \"no two different elements of the set are congruent to modulo m\".

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