19
3 and 11.
19
The numbers are: 2+7 = 9 and 2*7 = 14
To find positive integers that sum to 14 and have the smallest product, we can use the fact that the product of numbers is minimized when the numbers are as far apart as possible. The optimal way to split 14 is into one integer of 1 and the other of 13, resulting in the integers 1 and 13. The product of these two integers is (1 \times 13 = 13), which is the smallest possible product for integers that sum to 14.
For the product to be zero, one of the numbers must be 0. So the question is to find the maximum sum for fifteen consecutive whole numbers, INCLUDING 0. This is clearly achived by the numbers 0 to 14 (inclusive), whose sum is 105.
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The two numbers that have a product of 210 and a sum of 29 are 14 and 15. This can be verified since 14 × 15 = 210 and 14 + 15 = 29.
7 and 2
14, 35
The numbers are -15, and -14.
14 and 11
They are: 5 and 14