2012-4 Sum of squares

Find the smallest and the second smallest odd integers n satisfying the following property: \[ n=x_1^2+y_1^2 \text{ and } n^2=x_2^2+y_2^2 \] for some positive integers \(x_1,y_1,x_2,y_2\) such that \(x_1-y_1=x_2-y_2\).

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2012-4 Sum of squares, 4.1 out of 5 based on 21 ratings