Re: what is the best method to check if a number is a perfect square or not??

In article <wf8xkn7ehp.fsf@xxxxxxxxxxxxxxxxxxxx>,
Jón Fairbairn <jon.fairbairn@xxxxxxxxxxxx> wrote:
tchow@xxxxxxxxxxxxx writes:
Walter D. Stangl, Counting squares in Z_n, Math. Mag. 69 (1996), 285-289.
Thanks. That's surprisingly recent, too.

Well, this is the sort of thing that any number theorist could work out
if there were some need for it. If you take any textbook on elementary
number theory, it will have some chapter on quadratic residues and
quadratic reciprocity, and there will usually be some remarks about how
the general case ("mod n") reduces to the prime case ("mod p"). Then
they spend the bulk of the chapter on the prime case. How much detail
is given regarding the reduction from "mod n" to "mod p" will vary from
text to text; it is generally considered to be straightforward in
principle and not all that interesting to analyze in great detail,
unless there's some explicit reason for doing so.

The Stangl paper just happens to be the first reference I found which
gave the relevant formulas explicitly. There may be other places that
give the same formulas. To publish in the Mathematics Magazine, you
don't have to do original research; it just needs to be accessible to
mathematics undergraduates, and not be too hackneyed.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.