In \(\color{Purple}{\textbf{Chemistry}}\) you are allowed the following type of addition (the addition reaction) \[\mathrm{C+O_2 \implies CO_2}\]

But if you do it in \(\color{Blue}{\textbf{Maths}}\) for numbers,\[\displaystyle \color{Blue}{a+b=ab}\] it will be a \(\color{Red}{\textbf{big mistake!}}\)

But for how many pairs of \(\color{Green}{\text{integers (a,b)}}\) is the above said "\(\color{Red}{false}\)" property seen to be "\(\color{Green}{true}\)" ?

**Details and assumptions**:-

\(\bullet\) Here \(\textbf{ab}\) means \(a\times b\), not the representation in decimal system (i.e. \(ab\) is \(a\times b\) and \(\color{Red}{\mathrm{NOT}}\) \(10a+b\) )

This problem is a part of the set Mistakes Give Rise To Problems !!! .

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