FASTER SQUARE ROOTS MODULO A PRIME ON THE TI-89

This technique was formalized as TI-89 program sqrtmdp() in [9] and was used in [9] and [11] to assist in solving cubic and quartic congruences modulo a prime p. The purpose of this paper is to substantially improve the efficiency of the program sqrtmdp. First we review some of the ideas of the program sqrtmdp: In [10] we considered the problem of solving x ≡ δ (mod p). To quote from [10]: ―The Euler criterion says that if gcd(,p) =1 then  is a quadratic residue modulo p if