USAAAO — 2017 First Round

Consider that the absolute magnitude of a star is m₀. Imagine that the first star gets split into N smaller identical stars with the same temperature and average densities as the initial star, and that the sum of the masses of all N smaller stars is equal to the initial star’s mass (i.e., total mass is conserved). What is the total combined absolute magnitude (m) of all the N stars assuming that none of the stars obstruct each other’s light (i.e. their luminosities add linearly)?