Algebra of Concatenation cat() and multiplication & square of big numbers
Concatenation is a famous activity in computer programming and there are notation for this action as a function or a method like concat() in Excel or cat() in UNIX operating systems. Concatenation means link together in a series or chain. In Excel, the notation "&" is also used representing the operation of concatenation. Example is like "use"&"ful" will yield result "useful". The same result can be achieved by concat("use","ful"). For shortening the notation, we can use cat() in place of concat() for our discussion here. Now let us take subject of multiplication, where if two numbers are multiplied, how quickly, we get the result if we resort to concatenation process. Any number written in decimal system, say 25, is concatenation of certain unit digits. For 25, it is concatenation of 2 and 5. So concat(2,5) will give 25 or "2"&"5" will yield to 25. A two digit number having d...