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Find all n that can be expressed in such a way

Source: Chinese Mathematical Olympiad 2000 Problem 5

August 20, 2013
number theory unsolvednumber theory

Problem Statement

Find all positive integers nn such that there exists integers n1,…,nk≥3n_1,\ldots,n_k\ge 3, for some integer kk, satisfying n=n1n2⋯nk=212k(n1−1)⋯(nk−1)−1.n=n_1n_2\cdots n_k=2^{\frac{1}{2^k}(n_1-1)\cdots (n_k-1)}-1.
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