Hi Jasen! :-)

 JB> are there shorcuts to tell if a big integer (bignum) is not a square?
 JB> (like without trying to square-root it.)
Well, for integers, the last digit of any square is produced by squaring
the last digit of the square-root (modulo 10):

digit in root      digit in square
----------------------------------
     0                   0
     1                   1
     2                   4
     3                   9
     4                   6
     5                   5
     6                   6
     7                   9
     8                   4
     9                   1

Thus, no integer ending in 2, 3, 7, or 8 can be the square of any other
integer. This reduces the problem space by 40%. ;)

Ciao
Pascal

--- Msged/LNX 6.1.1