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15

Part of PEN A Problems

Problems(1)

A 15

Source:

5/25/2007
Suppose that k≥2k \ge 2 and n1,n2,⋯ ,nk≥1n_{1}, n_{2}, \cdots, n_{k}\ge 1 be natural numbers having the property n2  ∣  2n1−1,n3  ∣  2n2−1,⋯ ,nk  ∣  2nk−1−1,n1  ∣  2nk−1.n_{2}\; \vert \; 2^{n_{1}}-1, n_{3}\; \vert \; 2^{n_{2}}-1, \cdots, n_{k}\; \vert \; 2^{n_{k-1}}-1, n_{1}\; \vert \; 2^{n_{k}}-1. Show that n1=n2=⋯=nk=1n_{1}=n_{2}=\cdots=n_{k}=1.
number theoryleast common multipleDivisibility Theorypen