A quadric with arithmetic paucity

ISSN
0033-5606
Date Issued
2009
Author(s)
DOI
10.1093/qmath/han017
Abstract
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.