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a^k+b^k-1|a^n+b^n-1

Source: 2024IMOC

August 4, 2024
number theory

Problem Statement

Find all integers (a,b)(a,b) satisfying: there is an integer k>1k>1 such that ak+bk−1 ∣ an+bn−1a^k+b^k-1\ |\ a^n+b^n-1 holds for all integer n≥kn\geq k (we define that 0∣00|0)
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