Question

how many 4digit numbers are there with property that it is a square and the number obtained by increasing all its digits by 1 is als a square
(kvpy )

Answer 1

Let the two squares be a² and b².

We are told b²−a² = 1111

we can factor both sides of this equation to get:

we can factor both sides of this equation to get:(b−a)×(b+a)=11×101

so,

a = 101-11/2 = 45

b = 101+11/2 = 56

Numbers are :- 45² = 2025 & 56² = 3136 ..

[ONLY 1 VALUE POSSIBLE]

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