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What is the residue modulo 13 of the sum of the modulo 13 inverses of the first 12 positive integers?

Express your answer as an integer from 0 to 12, inclusive.

 Jan 7, 2019
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Modulo 13 inverses of the first 12 positive integers are:
1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12 =78 - Their total sum.
78 mod 13 =0 - Remainder.

 Jan 7, 2019

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