Thread: A quadric with arithmetic paucity

The quadric given by the equations x12 + x22 + x32 = y12 + y22 + y32, x1 + x2 + x3 = y1 + y2 + y3 has almost all its solutions with prime coordinates on the diagonals. This is shown in quantitative form. A similar statement holds for integral solutions whose coordinates can be written as the sum of two squares.



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Originally Posted by tom

The quadric given by the equations x12 + x22 + x32 = y12 + y22 + y32, x1 + x2 + x3 = y1 + y2 + y3 has almost all its solutions with prime coordinates on the diagonals. This is shown in quantitative form. A similar statement holds for integral solutions whose coordinates can be written as the sum of two squares.

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