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n^m | 5^{n^k} + 1

Source: 2015 VMEO IV Seniors 10.3 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2463156_2015_vmeo_iv

September 19, 2021
number theorydividesdivisible

Problem Statement

Given a positive integer kk. Find the condition of positive integer mm over kk such that there exists only one positive integer nn satisfying nm∣5nk+1,n^m | 5^{n^k} + 1,
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