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}.