For a positive integer n , let n denote the perfect square integer closest to n . For example, 74 =81 , 18 =16 . If N is the smallest positive integer such that 91 120 143 180 N =91.120 .143 .180 N find the sum of the squares of the digits of N .

Step-by-step solution

aligned & 10^2 11^2 12^2 13^2 N =91 120 143 180 N & 22 N =21 N aligned N is a perfect square. So, N must have a factor 21^2 . For least positive value of N , let N =21^2 So range of N will be, 21^2-20 N 21^2+21 aligned & 22.21^2=21 . N & N=21.22=462 aligned Sum of squares of digits =4^2+6^2+2^2=56