Some numbers have funny properties. For example: 89 --> 8¹ + 9² = 89 * 1 695 --> 6² + 9³ + 5⁴= 1390 = 695 * 2 46288 --> 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51 Given a positive integer n written as abcd... (a, b, c, d... being digits) and a positive integer p we want to find a positive integer k, if it exists, such that the sum of the digits of n taken to the successive powers of p is equal..