Freeflows

Planetary Invasion Puzzle

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?

1
2
3
+
4
5
6
-
7
8
9
$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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