  The results of a search for individual fast radio bursts with the Large
Phased Array of the Lebedev Physical Institute at 111 MHz during July 2012
through August 2018 are presented. The signals were distinguished by convolving
the data with a template with a fixed form, followed by convolution with test
dispersion measures. Areas of sky containing the galaxies M31 and M33 were
chosen for the search. Three radio bursts were detected in the vicinity of M33,
five in the vicinity of M31, and one in a region offset from the center of M31
by an hour in right ascension. The dispersion measures of the detected bursts
range from 203 to 1262 $ pc \cdot cm^{-3}$.
