The table below lists out all of the possible positive sums we can reach when adding factors of 42.
[tex]\begin{array}{|c|c|c|} \cline{1-3}a & b & a+b\\\cline{1-3}1 & 42 & 43\\\cline{1-3}2 & 21 & 23\\\cline{1-3}3 & 14 & 17\\\cline{1-3}6 & 7 & 13\\\cline{1-3}7 & 6 & 13\\\cline{1-3}14 & 3 & 17\\\cline{1-3}21 & 2 & 23\\\cline{1-3}42 & 1 & 43\\\cline{1-3}\end{array}[/tex]
For instance a*b = 2*21 = 42 and a+b = 2+21 = 23 shown in the 2nd row.
Now let's look at the negative sums.
[tex]\begin{array}{|c|c|c|} \cline{1-3}a & b & a+b\\\cline{1-3}-1 & -42 & -43\\\cline{1-3}-2 & -21 & -23\\\cline{1-3}-3 & -14 & -17\\\cline{1-3}-6 & -7 & -13\\\cline{1-3}-7 & -6 & -13\\\cline{1-3}-14 & -3 & -17\\\cline{1-3}-21 & -2 & -23\\\cline{1-3}-42 & -1 & -43\\\cline{1-3}\end{array}[/tex]
Unfortunately none of the items add to -1.
