Question: Prove that for any positive integers m and n, the check digit code in Z n m with check vector c = 1 = [1,

Prove that for any positive integers m and n, the check digit code in Zⁿ_mwith check vector c = 1 = [1, 1, . . . , 1] will detect all single errors. (That is, prove that if vectors u and v in Zⁿ_mdiffer in exactly one entry, Then c · u ≠ c · v .)

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