A four-digit number has the following properties:
(a) It is a perfect square;
(b) Its first two digits are equal
(c) Its last two digits are equal.
Find all such four-digit numbers. (RMO '91)
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2 Answers
106it is evidently divisible by 11
let the no be aabb
then dividing by 11 we get a0b which is again divisible by 11
so a+b equals 11
now u get only few options out of which 7744 satisfies perfect square
106(100a + b)/11
(100a + 11 - a)/11
9a + 1
this must be a perfect square u get only a is 7
