That might be relevant. Note however that not every n that's a square mod p and mod p^2 is also a square mod p^3 (consider n=5, p=2). Jim On Wed, Jul 17, 2019 at 4:51 PM Cris Moore <moore@santafe.edu> wrote:
There’s something called Henkel lifting that takes roots of equations mod p and turns them into roots mod p^k… does that help? - Cris
On Jul 17, 2019, at 2:43 PM, James Propp <jamespropp@gmail.com> wrote:
I’m pretty sure that a positive integer n that is a square mod p^k for all prime powers p^k must be a square in Q (as a consequence of the local-to-global principle for quadratic forms), from which it follows that n must be a square in Z.
But what if all we know is that n is a square mod p for every prime p? And what if we don’t know that n is positive?
This question was raised by Alaric Stephen (
https://aperiodical.com/2019/07/the-big-internet-math-off-2019-group-1-alex-...
).
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