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number theory

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February 2, 2017
number theoryalgebra

Problem Statement

Let k≥2k\geq 2,n1,n2,⋯ ,nk∈N+n_1,n_2,\cdots ,n_k\in \mathbb{N}_+,satisfied n2∣2n1−1,n3∣2n2−1,⋯ ,nk∣2nk−1−1,n1∣2nk−1n_2|2^{n_1}-1,n_3|2^{n_2}-1,\cdots ,n_k|2^{n_{k-1}}-1,n_1|2^{n_k}-1. Prove:n1=n2=⋯=nk=1n_ 1=n_ 2=\cdots=n_k=1.
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