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2-digit sabroso numbers wanted, perfect square

Source: 2020 Colombia day 1 p1

November 27, 2022
number theoryDigitsPerfect SquaresPerfect Square

Problem Statement

A positive integer is called sabroso if when it is added to the number obtained when its digits are interchanged from one side of its written form to the other, the result is a perfect square. For example, 143143 is sabroso, since 143+341=484=222143 + 341 =484 = 22^2. Find all two-digit sabroso numbers.