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There are several ways to approach this problem, but one possible solution is to count the number of integers between 1 and n that are divisible by either 3 or 5, and subtract from n the number of integers that are divisible by both 3 and 5 (i.e., multiples of 15). To count the number of integers that are divisible by 3 or 5, we could use the inclusion-exclusion principle. Let A be the set of integers that are divisible by 3, and let B be the set of integers that are divisible by 5. Then, the number of integers between 1 and n that are divisible by either 3 or 5 is: |A ∪ B| = |A| + |B| - |A ∩ B| where |A| is the cardinality (i.e., number of elements) of set A. In this case, we can compute |A| and |B| explicitly as follows: |A| = ⌊n/3⌋ (since every third integer is divisible by 3) |B| = ⌊n/5⌋ (since every fifth integer is divisible by 5) To compute |A ∩ B|, we need to count the number of integers that are divisible by both 3 and 5, i.e., by 15. This can be done by: |A ∩ B| = ⌊n/15⌋ (since every fifteenth integer is divisible by 15) Therefore, the number of integers between 1 and n that are divisible by either 3 or 5 is: |A ∪ B| = ⌊n/3⌋ + ⌊n/5⌋ - ⌊n/15⌋ Finally, we can subtract this number from n to get the answer: answer = n - (⌊n/3⌋ + ⌊n/5⌋ - ⌊n/15⌋) Note that in this formula, the floor function (⌊ ⌋) is used to round down to the nearest integer, since we want to count only integers between 1 and n. Also note that if n is itself a multiple of 3 or 5, we need to subtract it once more, since we have counted it twice.

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