Abstract
New results on the distribution of integral points on the cones $$ x_1^2 + x_2^2 + x_3^2 = y_1^2 + y_2^2 + y_3^2 $$ and $$ x_1^2 + x_2^2 + x_3^2 + x_4^2 = y_1^2 + y_2^2 + y_3^2 + y_4^2 $$ are obtained. Bibliography: 14 titles.
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