# How to Square an Integer a^2 - b^2 = (a+b)(a-b); a^2 = (a+b)(a-b) + b^2. Choose b as ['a' without the highest digit]. For example, if a=123 then b=23. If a=1947 then b=947. Thus 13579^2 = 10000 * 17158 + 3579^2 3579^2 = 3000 * 4158 + 579^2 579^2 = 500 * 658 + 79^2 79^2 = 70 * 88 + 9^2 9^2 = 81 Therefore 9^2 = 81 79^2 = 70 * 88 + 9^2 = 70 * 88 + 81 = 6241 579^2 = 500 * 658 + 79^2 = 500 * 658 + 6241 = 335241 3579^2 = 3000 * 4158 + 579^2 = 3000 * 4158 + 335241 = 12809241 13579^2 = 10000 * 17158 + 3579^2 = 10000 * 17158 + 12809241 = 1843 89241 To calculate 3000 * 4158, 12:3:15:24 = 12:3:17:4 = 12:4:7:4 = 1247 4 so 3000 * 4158 = 12474 * 1000 = 12474000.