What number does equal its square? Thus, what is the solution of the equation
You would answer they are 0 and 1! You may complain of such trivial question, but some peculiar ecology is existing in finite-digit systems sometimes.
Suppose that we limit the number of digits into 5 and that the equivalence is defined by the 5 digits in our number system. In this number system, we have another solution to (1) which is
Surely,
since the underlined (overflowed) part 8128 is neglected in our digit system ( 5-digit decimal system). This number is a part of well-known one by recreational mathematics mania. Indeed, we can extend the number into any n-digit system as
The question here is how we can derive such n-digit numbers in arbitrary base p (p-adic number system). We will discuss other extensions (such that a number equals its cube, etc) in other articles.
