Problem about squares

[Joshua Zucker]

I think you two are talking about different questions: Peter shows
it's not true that there exists such a number that works for all n but
David wants to know if, for each n, there exists a (not necessarily
the same) number.

--Joshua Zuker

On Jan 11, 2008 7:51 AM, Peter Pein <petsie at dordos.net> wrote:
> David W. Wilson schrieb:
> > Does there exist a non-square number which is square (mod 2^n) for every
> > n >= 0?
> >
> Call this non-square a0 and have a look at n0=ceil(log(a0)/log(2)). for every
> n>=n0: a0 == a0 mod 2^n and a0 has to be square and non-square simultaneously.
> cantradiction.
>
> P²
>