317,362 x 129,324 Is it even or odd
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The final result is x = 18.
Your question translates to computing .
Recall Euler's theorem: if (that is,
and
are relatively prime), then
, where
denotes Euler's totient function, which counts the number of positive integers relatively prime to
.
Since 13 is prime, we have . Then by Euler's theorem,
Now, observe that 2020 = 168×12 + 4, so that
and since 3⁴ = 81 = 6×13 + 3, we end up with
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.