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a_{n+1} equals the sum of tenth powers of decimal digits of a_n

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1993 p4

February 20, 2020

Sum of powersDigitsSumnumber theorySequence

Problem Statement

The sequence (

a_n

) of natural numbers is defined by

a_1 = 2

and

a_{n+1}

equals the sum of tenth powers of the decimal digits of

a_n

for all

n \ge 1

. Are there numbers which appear twice in the sequence (

a_n