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 s1=(−36)+(−1)=−37ab = 36 \ \\ s_{ 1 } = (-36) + (-1) = -37
ab=36  a1=1,b1=36,s1=37 a2=2,b2=18,s2=20 a3=3,b3=12,s3=15 a4=4,b4=9,s4=13 a5=6,b5=6,s5=12 a6=9,b6=4,s6=13 a7=12,b7=3,s7=15 a8=18,b8=2,s8=20 a9=36,b9=1,s9=37  a=36=6 b=36/a=36/6=6 s2=a+b=6+6=12ab = 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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