Post without words #24

Posted on January 15, 2019 by Brent

About Brent

Associate Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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5 Responses to Post without words #24

  1. Denis says:
    January 15, 2019 at 9:59 am

    Clearly something multiplicative or factor-based. I think the blue lines are primes, with 2 and 3 at the top point. Wondering about the mostly-red line near the bottom.

  2. blaisepascal2014 says:
    January 15, 2019 at 10:44 am

    By the structure (a triangle), it feels like it is the result of some function f(i,j), j < i. The blue lines look like they are when i is prime.
    Since the "words" (aka "tags") attached include Carmichael, Fermat, primality, and test, I'm going to guess that the colors correspond to values of j^{i-1} \mod i. Fermat's Little Theorem states that if i is prime, then j^{i-1} \equiv 1 \mod i for all j.
    That would account for the blue lines (1) for each prime row. I would guess that the 561st row is red. 561 is the first Carmichael number, which is composite but "passes" Fermat's Little Theorem.

    • Brent says:
      January 15, 2019 at 11:17 am

      Right, except the colors are more “logical” than numerical. I.e. the colors don’t correspond directly to the value of j^{i-1} \bmod i; there are four different colors that encode something about the pair (i,j).

  3. Pingback: Fermat witnesses and liars (some words on PWW #24) | The Math Less Traveled

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