Re: Zero digits in powers

In article <15364-42B76153-906@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> ol3@xxxxxxxxx (Oscar Lanzi III) writes:
> *** T. Winter makes a valid point. When you use a probabilistic model,
> you're really guessing when you have accurately identified a sample
> space. In the fifth-power summation example, the factorization in the
> formula happesn to give enough information for the proabilistic model to
> identify the right proposition.

Yes, in that case. However, there is *no* way that it shows that it
actually *is* the right proposition.

> Probabilistc models can give an idea of
> what might be most fruitful to try to prove -- but if in the process of
> solving the problem you come across new information, you need to
> reevaulate your probabilistic expectations in light thereof.

Indeed. The probabilistic method only gives an indication of what might
be true. It can not replace a proof.

> Incidentally, 34N^2-1 is always congruent with 5 or 7 modulo 8. There
> you have it.

Indeed. Nothing probabilistic about it.

And back to the original. When you are looking at powers of 2, decimally
written, I do not think there is a probabilistic proof strong enough to
show that there is a largest power where there is no 0 in the expansion.
These kinds of (number theoretical) problems are beyond the capacities of
probability.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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