in a solar system of $n$ planets, zorn the world conqueror can invade $m$ planets at a time, but once there are less than $m$ free worlds left, he stops. if he invades $13$ at a time then there are $6$ left, and if he invades $14$ at a time then there are $5$ left. if this solar system has more than $100$ planets, what is the smallest number of planets it could have?

The smallest number of planets is 201.Let N be the number of planets in the solar systemN(mod 13)= 6N(mod 14) = 513 and 14 have no common factor so any solution will be of the formx = r + 13 . 14k= r + 182k, r ,k ∈NWe can eyeball that 19 is a solution and so all solutions will beN = 19 + 182k and the first of these such that N> 100 is N = 19 + 182    = 201Therefore the smallest number of planets it could have is 201.To know more about the solar system refer to the link given below:https://brainly.com/question/1286910#SPJ4