Abstract
The happy function S of each positive integer x is defined to be the sum of the squares of the decimal digits of x. For example, S(2) = 4 and S(123) = 12 + 22 + 32 = 14. It is well known that for any , there exists such that , where S(n) is the n-fold composition of S. In addition, if and for some , then x is called a happy number.
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