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How to check whether an infinite set is closed under addition?


Given k positive numbers a_1<a_2<a_3<...<a_k, and all integers greater
than a_k, we want to check whether this set {a_1, a_2, a_3,...a_k, a_k
+ 1, a_k+2, ......} is closed under addition.

Is there any easy way to do this? any functions that we could use in
Mathematica?

Your help will be greatly appreciated.




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