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Find such numbers

Source: MTRP 2019 Class 11-Short Answer Type Problems: Problem 4 :-

April 9, 2020
number theory

Problem Statement

Are there infinitely many natural numbers nn such that the sum of 2019th powers of the digits of nn is equal to nn ? You don't need to find any such nn. Just provide mathematical justi fication if you think there are in finitely many or finitely many such natural numbers
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