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Algebra |
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Authors: Shuojie Yuan
This paper studies the positive integer solutions of an exponential Diophantine equation of the following form: 3^aX+3^{a-1}+3^{a-2}times2^{b_1}+3^{a-3}times2^{b_1+b_2}ldots+3^{a-a}times2^{b_1+b_2+ldots+b_{a-1}}}{2^{b_1+b_2+ldots+b_a}}=X，where a,X,b_iare positive integers andb_igeq1. This equation arises from the analysis of the cyclic structure of a specific iterative sequence. Through rigorous algebraic derivation and inequality analysis, this paper proves that for any given ageq1 and all sequences of b_i satisfying the conditions, the only positive integer solution to this equation is X=1 . This conclusion reveals the uniqueness of the solution for this class of equations.
Comments: 5 Pages.
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[v1] 2025-11-16 00:04:19
[v2] 2025-11-29 02:19:28
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