integer square roots

[Mensanator]

On Jul 23, 7:11 pm, Mensanator <mensana... at aol.com> wrote:
> On Jul 23, 6:02 pm, timro21 <timr... at gmail.com> wrote:
>
> > I wish to process billions of 100-digit numbers and test if each has
> > an integer square root.  What's the most efficient way to do this?
>
> Use gmpy.
>
> >>> import gmpy
> >>> help(gmpy.sqrt)
>
> Help on built-in function sqrt in module gmpy:
>
> sqrt(...)
>     sqrt(x): returns the integer, truncated square root of x, i.e. the
>     largest y such that x>=y*y. x must be an mpz, or else gets coerced
>     to one; further, x must be >= 0.
>
> >>> p = 10**100
> >>> p1 = gmpy.next_prime(p)
> >>> p1
>
> mpz
> (10000000000000000000000000000000000000000000000000000000000000000000000000­000000000000000000000000267)
>
> >>> gmpy.sqrt(p1)
>
> mpz(100000000000000000000000000000000000000000000000000)

Duh. I completely misread this. I thought you wanted the square root,
not IF it had a square root that's an integer.

Sorry about that.

Try this, instead:

>>> gmpy.sqrtrem(p1)
(mpz(100000000000000000000000000000000000000000000000000), mpz(267))

It has a non-zero remainder, so it's not an integer square root.