Congratulations to all three, specially to Paul and Dickson, that proved the number (solution) achieved by Lisa, to be the minimum.
We have :
1090 + X = A^2
1090 * X = B^2
Since 1090 has no square factor > 1, 1090 must be (by the second equation above) a factor of X; in fact, X must be of the form 1090*C^2.
Thus, A^2 = 1090 + 1090 * C^2 = 1090*(C^2 + 1).
By similar reasoning, 1090 is a factor of (C^2 + 1). The smallest value of C^2 wich makes (C^2 + 1) divisible by 1090 is 1089, wich, fortunately, happens to be a perfect square, i.e., 33^2.
Hence, X = 1090 * 1089 = 1,187,010.
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