# Two integers

Two integers, a and b, have a product of 36. What is the least possible sum of a and b?

Correct result:

s1 =  -37
s2 =  12

#### Solution:

$ab=36 \ \\ s_{1}=(-36) + (-1)=-37$
$ab=36 \ \\ \ \\ a_{1}=1, b_{1}=36, s_{1}=37 \ \\ a_{2}=2, b_{2}=18, s_{2}=20 \ \\ a_{3}=3, b_{3}=12, s_{3}=15 \ \\ a_{4}=4, b_{4}=9, s_{4}=13 \ \\ a_{5}=6, b_{5}=6, s_{5}=12 \ \\ a_{6}=9, b_{6}=4, s_{6}=13 \ \\ a_{7}=12, b_{7}=3, s_{7}=15 \ \\ a_{8}=18, b_{8}=2, s_{8}=20 \ \\ a_{9}=36, b_{9}=1, s_{9}=37 \ \\ \ \\ a=\sqrt{ 36 }=6 \ \\ b=36/a=36/6=6 \ \\ s_{2}=a + b=6 + 6=12$

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