[seqfan] Re: Fwd: Your A051217 Nonnegative numbers of the form 6^x-y^2.
Maximilian.Hasler at martinique.univ-ag.fr
Thu Nov 17 14:58:26 CET 2011
On Wed, Nov 16, 2011 at 6:11 PM, Vladimir Shevelev <shevelev at bgu.ac.il> wrote:
> I agree with David: the sequence is, of course, well-defined.
> But it is clear that without an upper estimate for x it cannot be computable.
No, this is not clear.
Using modular arithmetics you may be able to show that there is no
solution (if there is none).
(Hint: Both the set of quadratic residues y^2 and the range of 6^x are
finite (and "usually" a strict subset of) Z/mZ, so with some luck the
possible differences are also a strict subset of Z/mZ.)
E.g., the expression 6^x-y^2 can never be equal to 3,4,8 or 9 (mod 10),
so the sequence cannot contain any number ending in 3,4,8 or 9.
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