Notes

Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations


Large solutions [to Diophantine equations]

A few other 2-variable equations with fairly large smallest solutions are:

x^3 == 3*y^3 -x y + 63: {7149, 4957}

x^4 == y^3 + 2 x y - 2 y + 81: {19674, 531117}

x^4 == 5*y^3 + x y + y - 8 x: {69126, 1659072}

The equation x^x y^y == z^z is known to have smallest non-trivial solution {2985984, 1679616, 4478976}.


From Stephen Wolfram: A New Kind of Science [citation]