A theorem on the distribution of quadratic residues having applications in the ergodic method of Yu. V. Linnik

A theorem is proved which is used in the next paper of the collection. In the paper the following theorem is proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 50, pp. 169–178, 1975.I wish to thank A. V. Malyshev for posing the problem and for attention to the work and D. N. Andreev for help in reviewing the paper of A. I. Vinogradov and Yu. V. Linnik.