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For example
25 = 02 + ( ±5)2 = ( ±5)2 + 02 = ( ±3)2 + ( ±4)2 = ( ±4)2 + ( ±3)2
and this shows that there are 12 points with integer coordinates on the circle x2+ y2 = 52 with centre at the origin and radius 5 units.