Let φ1, . . . , φn (n ≥ 2) be nonzero integers such that the equation ∑n i=1 φix2 i = 0 is solvable in integers x1, . . . , xn not all zero. It is shown that there exists a solution satisfying 0 < ∑n i=1 |φi|x2 i ≤ 2|φ1 ⋯ φn|, and that the constant 2 is best possible.

Additional Metadata
Keywords Diagonal quadratic forms, Small solutions
Journal Canadian Journal of Mathematics
Citation
Ou, Z.M. (Zhiming M.), & Williams, K.S. (2000). Small solutions of φ1x2 1 + ⋯ + φnx2 n = 0. Canadian Journal of Mathematics, 52(3), 613–632.