A 4 digit number a perfect square 1 added to each digit becomes a square. Find the number
Let the number be x^2 none of digits = 9
adding 1111 makes it a perfect square say y^2
x^2+1111 = y^2
so y^2 – x^2 = 1111
(y-x) (y+x) = 11 * 101
As 11 and 101 are primes 1111 can be factored only as above other than 1 * 1111
So y – x = 11 and y+x = 101
Add 2 get 2y= 112 or y = 56 and x = 45
x^2 = 2025 and adding 1111 we get y^2(56^2) = 3036
