2008/011) A 4 digit number a perfect square 1 added to each digit becomes a square.

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