[ox_n]

Consecutive base numbers will necessarily alternate between even and odd. So even the closest base numbers still have a gap between their resulting odd number series, which only increases as the distance between base numbers increases.

[andrepd]

Still don't get it. What do you mean by "base numbers" and what do you mean by "alternate between even and odd"?

[gowld]

'ox_n appears to be trying to prove (by a pigeonhole agument) that the equation x^n + y^n = z^n in unsolvable for _some z_. That's much weaker than proving that it is unsatisfiable at _every_ z.