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number theory

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January 31, 2016
number theory

Problem Statement

In a sequence ,first term is 22 and after 2.2. term all terms is equal to sum of the previous number's digits' 5.5. power. (Like this 2.2.term is 25=322^5=32 , 3.3.term is 35+25=243+32=275⋯3^5+2^5=243+32=275\dotsm) Prove that, this infinite sequence has at least 22 two numbers are equal.
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