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Part of 1985 IMO Longlists

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Very nice number theory - Show that n_i=1

Source:

9/14/2010
Let k≥2k \geq 2 and n1,n2,...,nk≥1n_1, n_2, . . . , n_k \geq 1 natural numbers having the property n2∣2n1−1,n3∣2n2−1,⋯ ,nk∣2nk−1−1n_2 | 2^{n_1} - 1, n_3 | 2^{n_2} -1 , \cdots, n_k | 2^{n_k-1}-1, and n1∣2nk−1n_1 | 2^{n_k} - 1. Show that n1=n2=⋯=nk=1.n_1 = n_2 = \cdots = n_k = 1.
number theory unsolvednumber theory