IMO 1985 LL ROM67

Let k \geq2 and n1, n2, . . . , nk \geq1 natural numbers having the

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IMO 1985 LL ROM67

Origin: ROM

Problem

Let k \geq2 and n1, n2, . . . , nk \geq1 natural numbers having the property n2 | 2n1 −1, n3 | 2n2 −1, . . . , nk | 2nk−1 −1, and n1 | 2nk −1. Show that n1 = n2 = \cdot \cdot \cdot = nk = 1.