a) the mirror is large enough to reflect enough sunlight to light an entire city;
b) the energy density of the sun that lights it up in the day is 'n'
c) you want to reflect 'n * m' energy for night-time visibility, where 'm' represents the fraction of daylight brightness you want at night
d) the surface area of your mirror must be 'city area' x 'n' x 'm', with extra factors added in for reflectivity and atmospheric losses.
Right idea, but "n" doesn't appear in the final equation. If it's transferring all incident sunlight then the incident power density simply cancels. Atmospheric loses are partly factored in already too, the sun's light has to come through it, angle obviously varies, but it does this during the day, leaving city area * m as the important bit. The fact sensitivity is approximately logarithmic should help a lot though, 1/100th the light power wont run a solar farm, but incident solar irradiation is usually taken at roughly 1kW/m2, yet a 20W LED bulb can light a reasonable sized room. On the negative side, area is of course square with dimension, so 1/100th the incident power requires 1/10th the diameter of the area you're trying to illuminate.
Still sceptical, it has a pipe-dream feel to it, but not physically impossible.