Question 1106395
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1, 3, and 9.<br>
If the sum of the three numbers and the sum of the squares of the three numbers are both integers, then each of the numbers is almost certain to be an integer.<br>
A very little time playing with geometric progressions of three integers finds the answer.<br>
If you need an algebraic solution, re-post the question, specifying that you need an algebraic solution.