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For natural numbers and if objects are distributed among sets, then the Pigeonhole Principle asserts that at least one of the sets will contain at least objects.
Let us consider the partition of the set ito 5 subset: , , and The sum of elements in each subset is equal to 15. Taking into account that there are 5 subsets and we choose 6 elements by Pigeonhole Principle we get that at least one pair will be selected. Consequently, there must be two integer whose sum is fifteen.