# Two integers

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

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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