13^88/19 = (-6)^88/19 (13 could be written as 19-6 which gives -6 as a remainder)
= ((-6)^2)^44/19 = 36^44/19
= (38-2)^44/19
= (-2)^44/19 = 16^11/19 = (-3)^11/19
= -3 * (-3)^10/19 = -3 * 9^5/19 = -3 * 9 * 9^4/19 = -3 * 9 * (81)^2/19
= -3 * 9 * (76-5)^2/19 = -3 * 9 * (-5)^2/19 = -3 * 9 * 25 /19
= -27 * 6/19 = -8 * 6/19 = -48 /19 = -10/19 = (-19 + 9 ) / 19 = 9 is the remainder