Given,3737+37=(38)37+37=−(1−38)2+37(1−x)n=1−nx+n(n−1)x /2...... Thus, (1−38)37 = 1 – 37 × 38 …. All other term will contain 38. = - (1 – terms containing 38 as a factor) + 37 = terms containing 38 as a factor + 36 Thus when the above number is divided by 38, remainder will be 36.