sidef-scripts/Math/modular_tetration.sf

#!/usr/bin/ruby

# Modular computation of the tetration operation, using Euler's theorem.

# See also:
#   https://en.wikipedia.org/wiki/Tetration
#   https://www.youtube.com/watch?v=vzhzwLp_qrs

func tetration(a, b, m) {

    return 0 if (m == 1)
    return 1 if (b == 0)

    powmod(a, __FUNC__(a, b-1, m.euler_phi), m)
}

for n in (2 .. 1000) {
    var k = n.prime
    if (tetration(10, 10, k) + 23 % k == 0) {
        say "#{'%3s' % k} | (10∆10 + 23)"
    }
}

__END__
  3 | (10∆10 + 23)
 13 | (10∆10 + 23)
673 | (10∆10 + 23)