Powers of 12 modulo 19

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Tuesday, December 11, 2018 

On Tuesday, mathematicians who specialize in prime numbers and modular arithmetic are celebrating a special date. Today, mathematicians around the world will mark 7:08:01 a.m. in their respective time zones because the numerical name for that moment is 12/11/18, 07:08:01. These are the powers of twelve modulo 19.

12² = 144, which is congruent to 11 modulo 19.

12³ = 1,728, which is congruent to −1 or 18 modulo 19.

12⁴ = 20,736, which is congruent to 7 modulo 19.

12⁵ = 248,832, which is congruent to 8 modulo 19.

12⁶ = 2,985,984, which is congruent to 1 modulo 19.

Twelve has a multiplicative order of 6 because the repeating sequence has 6 terms: 12, 11, 18, 7, 8, 1, and those six numbers repeat infinitely.

Sources

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