Logging to /Users/s/tmp/pari-03.25
GPRC Done.

              GP/PARI CALCULATOR Version 2.13.1 (released)
      i386 running darwin (x86-64/GMP-6.2.1 kernel) 64-bit version
 compiled: Jan 25 2021, Apple clang version 12.0.0 (clang-1200.0.32.28)
                        threading engine: single
             (readline v8.1 enabled, extended help enabled)

                 Copyright (C) 2000-2020 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, 
and comes WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisizemax = 900001792, primelimit = 1000000
(13:51) gp > 18541^2-12709^2
%1 = 182250000
(13:51) gp > issquare(%)
%2 = 1
(13:51) gp > issquare(18541^2-12709^2)
%3 = 1
(13:51) gp > ?issquare
issquare(x,{&n}): true(1) if x is a square, false(0) if not. If n is 
given puts the exact square root there if it was computed.

(13:51) gp > ??issquare
issquare(x,{&n}):

   True (1) if x is a square, false (0) if not.   What "being a square"
means  depends on the type of x: all t_COMPLEX are squares,  as well as
all  nonnegative  t_REAL;    for exact types such as t_INT,  t_FRAC and
t_INTMOD,  squares are numbers of the form s^2 with s in Z,  Q and Z/NZ
respectively.

   ? issquare(3)          \\ as an integer
   %1 = 0
   ? issquare(3.)         \\ as a real number
   %2 = 1
   ? issquare(Mod(7, 8))  \\ in Z/8Z
   %3 = 0
   ? issquare( 5 + O(13^4) )  \\ in Q_13
   %4 = 0

   If n is given, a square root of x is put into n.

   ? issquare(4, &n)
   %1 = 1
   ? n
   %2 = 2

   For polynomials,  either we detect that the characteristic is 2 (and
check  directly  odd  and even-power monomials)  or we assume that 2 is
/*-- (type RETURN to continue) --*/
invertible  and  check  whether squaring the truncated power series for
the square root yields the original input.

   For  t_POLMOD  x,   we  only support t_POLMODs of t_INTMODs encoding
finite  fields,  assuming without checking that the intmod modulus p is
prime and that the polmod modulus is irreducible modulo p.

   ? issquare(Mod(Mod(2,3), x^2+1), &n)
   %1 = 1
   ? n
   %2 = Mod(Mod(2, 3)*x, Mod(1, 3)*x^2 + Mod(1, 3))

   The library syntax is long issquareall(GEN x, GEN *n = NULL).   Also
available is long issquare(GEN x). Deprecated GP-specific functions GEN
gissquare(GEN x) and GEN gissquareall(GEN x,  GEN *pt) return gen_0 and
gen_1 instead of a boolean value.

(13:54) gp > issquare(18541^2-12709^2)
%4 = 1
(13:54) gp > sqrt(18541^2-12709^2)
%5 = 13500.000000000000000000000000000000000
(13:54) gp > 12709^2
%6 = 161518681
(13:54) gp > 13500^2
%7 = 182250000
(13:54) gp > 18541^2
%8 = 343768681
(13:54) gp > 12709^2+13500^2==18541^2
%9 = 1
(13:55) gp > 12709^2+13500^2-18541^2
%10 = 0
(13:55) gp > factor(13500)
%11 = 
[2 2]

[3 3]

[5 3]

(13:55) gp > 2^2*3^3*5^3
%12 = 13500