



 
The standard way to answer questions like this is to use "modular arithmetic". The idea is that every integer is equal to There are shorter notations that we can use here. We can say (eg) 26 is "equivalent to 2 modulo 6", or we can say it belongs to the equivalence class [2]. Now work case by case. For instance, [2]^{3} = [2][4] = [2] (the class containing 8) Do the same for [0],[1],[3],[4],[5] and you're done. It's hardly worth doing here, but for numbers that aren't prime powers you can factor and check each individually: in other words, to show x^{3} + 11x is divisible by 6, show it's divisible by 2 and by 3. Good Hunting!  


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