Let b≥2 be a positive integer.(a) Show that for an integer N, written in base b, to be equal to the sum of the squares of its digits, it is necessary either that N=1 or that N have only two digits.(b) Give a complete list of all integers not exceeding 50 that, relative to some base b, are equal to the sum of the squares of their digits.(c) Show that for any base b the number of two-digit integers that are equal to the sum of the squares of their digits is even.(d) Show that for any odd base b there is an integer other than 1 that is equal to the sum of the squares of its digits. quadraticsalgebranumber theory unsolvednumber theory